Wave Simulation in Frozen Porous Media

Carcione, José M.; Seriani, G.

doi:10.1006/jcph.2001.6756

Cited by 82 publications

(77 citation statements)

References 24 publications

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“…In fact, no matter from macroor micro-mechanics, these theories have no essential differences (Li and Li, 1989). Due to its general and rather fundamental character, Biot's theory has been extended in dealing with different problems (Piekarski and Munro, 1977;Leclaire et al, 1994;Berryman and Wang, 2000;Carcione and Seriani, 2001). In this paper, Biot's theory is adopted to deal with energy propagation in anisotropic porous materials.…”

Section: Background Theorymentioning

confidence: 99%

Wave propagation and critical conditions for energy focusing pattern transformation in anisotropic fluid-filled porous structures

Liu

Gao

2008

International Journal of Solids and Structures

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a b s t r a c tConsidering the pore fluid, the energy singular propagation in open-cell anisotropic porous solids is studied with the aim to provide a reference in the energy design and application of porous materials. Firstly, based on Biot's theory, the perturbed eigenvalue problem that arises when the nearly pure modes are propagated is considered. Then, by using the obtained perturbed eigenvalues, the evolution conditions on the elastic parameters of solid skeleton materials are established for the existence of various systems of folds in the wave front. The emphasis is placed on the slow wave, which is particular for the porous material with the pore fluids. The critical conditions for the pattern transformation in the parameter space are given for the first time. Finally, the special situation (zero porosity) is discussed and the comparison with respect to the results for pure solids is made. The results show that the situation in the pure solids is a degenerated case of the present discussion.

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Section: Background Theorymentioning

confidence: 99%

Wave propagation and critical conditions for energy focusing pattern transformation in anisotropic fluid-filled porous structures

Liu

Gao

2008

International Journal of Solids and Structures

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“…8 In the last two articles, the interaction between sand grains and ice has been included and, in addition, the stiffening of the rock frame due to grain cementation by ice at freezing temperatures. The three-dimensional equations of momentum conservation can be expressed as…”

Section: A Conservation Of Momentummentioning

confidence: 99%

“…Expressions of the physical quantities are given in Appendix A, and their physical meaning is explained in Carcione and Tinivella 2 and Carcione and Seriani. 6,8 The analysis in Appendix B shows that the relative displacement of the fluid relative to the rock and ice frames ͑taken as a composite͒ is…”

Section: A Conservation Of Momentummentioning

confidence: 99%

“…However, the Lagrangian formulation used by Leclaire et al 7 and, consequently, the differential equations solved by Carcione and Seriani, 8 hold for uniform porosity, since the average displacements of the solid and fluid phases are used as Lagrangian coordinates and the respective stress components are used as generalized forces. These equations are analogous to Biot's 1956 equations describing wave propagation in a two-phase porous medium, 9 which hold for constant porosity.…”

Section: Introductionmentioning

confidence: 99%

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Wave simulation in partially frozen porous media with fractal freezing conditions

Carcione

Santos

Ravazzoli

et al. 2003

Journal of Applied Physics

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Melting/freezing behavior of a fluid confined in porous glasses and MCM-41: Dielectric spectroscopy and molecular simulation J. Chem. Phys. 114, 950 (2001); 10.1063/1.1329343 Freezing of simple fluids in microporous activated carbon fibers: Comparison of simulation and experiment J. Chem. Phys. 111, 9058 (1999); 10.1063/1.480261Freezing and melting of water in a single cylindrical pore: The pore-size dependence of freezing and melting behavior A recent article ͓J. M. Carcione and G. Seriani, J. Comput. Phys. 170, 676 ͑2001͔͒ proposes a modeling algorithm for wave simulation in a three-phase porous medium composed of sand grains, ice, and water. The differential equations hold for uniform water ͑ice͒ content. Here, we obtain the variable-porosity differential equations by using the analogy with the two-phase case and the complementary energy theorem. The displacements of the rock and ice frames and the variation of fluid content are the generalized coordinates, and the stress components and fluid pressure are the generalized forces. We simulate wave propagation in a frozen porous medium with fractal variations of porosity and, therefore, realistic freezing conditions.

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“…Wave propagation in composite porous materials has applications in many branches of science and technology, such as seismic methods in the presence of shaley sandstones [8], frozen or partially frozen sandstones [29,10,11], gas-hydrates in ocean-bottom sediments [12], and evaluation of the freezing conditions of foods by ultrasonic techniques [26]. A recent review of the theory of wave propagation in fluid-saturated porous media can be found in [7].…”

Section: Introductionmentioning

confidence: 99%

Finite Element Methods for the Simulation of Waves in Composite Saturated Poroviscoelastic Media

Santos¹,

Sheen²

2007

SIAM J. Numer. Anal.

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Abstract. This work presents and analyzes a collection of finite element procedures for the simulation of wave propagation in a porous medium composed of two weakly coupled solids saturated by a single-phase fluid. The equations of motion, formulated in the space-frequency domain, include dissipation due to viscous interaction between the fluid and solid phases with a correction factor in the high-frequency range and intrinsic anelasticity of the solids modeled using linear viscoelasticity. This formulation leads to the solution of a Helmholtz-type boundary value problem for each temporal frequency. For the spatial discretization, nonconforming finite element spaces are employed for the solid phases, while for the fluid phase the vector part of the Raviart-Thomas-Nedelec mixed finite element space is used. Optimal a priori error estimates for global standard and hybridized Galerkin finite element procedures are derived. An iterative nonoverlapping domain decomposition procedure is also presented and convergence results are derived. Numerical experiments showing the application of the numerical procedures to simulate wave propagation in partially frozen porous media are presented.Key words. poroviscoelasticity, finite element method, error estimate, domain decomposition AMS subject classifications. 65C20, 65N30, 65N55, 86-08 DOI. 10.1137/050629069 1. Introduction. Wave propagation in composite porous materials has applications in many branches of science and technology, such as seismic methods in the presence of shaley sandstones [8], frozen or partially frozen sandstones [29, 10, 11], gas-hydrates in ocean-bottom sediments [12], and evaluation of the freezing conditions of foods by ultrasonic techniques [26]. A recent review of the theory of wave propagation in fluid-saturated porous media can be found in [7].A theory to describe wave propagation in frozen porous media was first presented by Leclaire, and Aguirre Puente [24]. This model, valid for uniform porosity, predicts the existence of three compressional and two shear waves; the verification that additional (slow) waves can be observed in laboratory experiments was published by Leclaire, and Aguirre Puente [25]. Later, Carcione and Tinivella [12] generalized this theory to include the interaction between the solid and ice particles and grain cementation with decreasing temperature, used as a parameter to determine the bulk water content. Also, Carcione, Gurevich, and Cavallini [8] applied this theory to study the acoustic properties of shaley sandstones, assuming that sand and clay are nonwelded and form a continuous and interpenetrating porous composite skeleton. Both frozen porous media and shaley sandstones are examples of porous materials where the two solid phases are weakly coupled or nonwelded, i.e., both solids form a continuous and interacting composite structure, interchanging mechan-

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Wave Simulation in Frozen Porous Media

Cited by 82 publications

References 24 publications

Wave propagation and critical conditions for energy focusing pattern transformation in anisotropic fluid-filled porous structures

Wave propagation and critical conditions for energy focusing pattern transformation in anisotropic fluid-filled porous structures

Wave simulation in partially frozen porous media with fractal freezing conditions

Finite Element Methods for the Simulation of Waves in Composite Saturated Poroviscoelastic Media

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