A 3-D HIERARCHICAL FE FORMULATION OF BIOT'S EQUATIONS FOR ELASTO-ACOUSTIC MODELLING OF POROUS MEDIA

2001 ◽  
Vol 245 (4) ◽  
pp. 633-652 ◽  
Author(s):  
N.-E. HÖRLIN ◽  
M. NORDSTRÖM ◽  
P. GÖRANSSON
Keyword(s):  
Porous Media ◽  
Acoustic Modelling ◽  
Biot’S Equations

Analytical Solution of Biot's Equations Based on Potential Functions Method

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
Abolfazl Hasani Baferani ◽  
Abdolreza Ohadi
Keyword(s):  
Porous Media ◽  
Analytical Solution ◽  
Differential Equations ◽  
Porous Materials ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Potential Functions ◽  
Basic Field ◽  
Acoustical Properties ◽  
Biot’S Equations

In this paper, a new analytical solution for Biot's equations is presented based on potential functions method. The primary coupled Biot's equations have been considered based on fluid and solid displacements in three-dimensional (3D) space. By defining some potential functions, the governing equations have been improved to a simpler form. Then the coupled Biot's equations have been replaced with four-decoupled equations, by doing some mathematical manipulations. For a case study, it is assumed that the incident wave is in xy-plane and for specific boundary conditions; the partial differential equations are converted to ordinary differential equations and solved analytically. Then two foams with different properties have been considered, and acoustical properties of these foams due to the new developed method have been compared with the corresponding results presented by transfer-matrix method. Good agreement between results verifies the new presented solution. Based on the potential function method, not only the acoustical properties of porous materials are calculated, but also the analytical values of all basic field variables, such as pressure, fluid, and solid displacements, are obtained for all points in the porous media. Furthermore, fundamental features, such as damped and undamped natural frequencies, and damping coefficient of porous materials are calculated by considering presented results. The obtained results show that maximum values of field variables, such as pressure, fluid, and solid displacements, happen at the damped natural frequencies of the porous media, as expected. By increasing material thickness, the effect of damping of porous material on damped natural frequency decreases. Damping decreases the first natural frequency of the foam up to 8.5%.

ACOUSTIC LOGGING MODELING BY REFINED BIOT'S EQUATIONS

2000 ◽  
Vol 11 (02) ◽  
pp. 365-396 ◽  
Author(s):  
BORIS D. PLYUSHCHENKOV ◽  
VICTOR I. TURCHANINOV
Keyword(s):  
Porous Media ◽  
Finite Difference ◽  
Difference Scheme ◽  
External Surface ◽  
Modern Theory ◽  
Acoustic Logging ◽  
Local Boundary ◽  
Dynamic Permeability ◽  
Conservative Finite Difference Scheme ◽  
Biot’S Equations

An explicit uniform completely conservative finite difference scheme for the refined Biot's equations is proposed. This system is modified according to the modern theory of dynamic permeability and tortuosity in a fluid-saturated elastic porous media. The approximate local boundary transparency conditions are constructed. The acoustic logging device is simulated by the choice of appropriate boundary conditions on its external surface. This scheme and these conditions are satisfactory for exploring borehole acoustic problems in permeable formations in a real axial-symmetrical situation. The developed approach can be adapted for a nonsymmetric case also.

On: “Elastic properties of unconsolidated porous sand reservoirs,” by S. N. Domenico (GEOPHYSICS, December 1977, p. 1339–1368).

Geophysics ◽  
1979 ◽  
Vol 44 (4) ◽  
pp. 830-831 ◽  
Author(s):  
R. J. S. Brown ◽  
J. Korringa
Keyword(s):  
Porous Media ◽  
Elastic Properties ◽  
Acoustic Waves ◽  
Glass Bead ◽  
Coupling Factor ◽  
Saturated Porous Media ◽  
Extensive Discussion ◽  
Acoustic Velocities ◽  
Fluid Saturated Porous Media ◽  
Biot’S Equations

Domenico gives a valuable set of data on acoustic velocities in a sand pack and a glass bead pack with various brine saturations and various pressures. There are, however, two difficulties with the extensive discussion of the data in terms of the fluid‐solid coupling factor k in Biot’s equations for acoustic waves in fluid‐saturated porous media, and there is given a wrong relationship among some compressibilities. We are addressing these points and not reviewing the paper as a whole.

Analytical investigation of the acoustic behavior of nanocomposite porous media by using modified nonlocal Biot’s equations

2017 ◽  
Vol 24 (13) ◽  
pp. 2701-2716 ◽  
Author(s):  
A Hasani Baferani ◽  
AR Ohadi
Keyword(s):  
Porous Media ◽  
Absorption Coefficient ◽  
Nonlocal Parameter ◽  
Nonlocal Elasticity Theory ◽  
Analytical Investigation ◽  
Considerable Effect ◽  
Acoustical Properties ◽  
Coefficient Increase ◽  
Biot’S Equations ◽  
Good Agreement

In this paper, the modified Biot’s equations based on nonlocal elasticity theory are presented for modeling nanocomposite porous media. The analytical solution of modified Biot’s equations is obtained by using the recently developed potential function method. By doing some mathematical manipulation, the coupled modified Biot’s equations are converted to two decoupled equations. Consequently, the variations of field variables and acoustical properties of a considered nanocomposite foam are studied by changing the nonlocal parameter. The obtained results show that the local Biot’s results are in good agreement with the nonlocal modified Biot’s results for very small values of the nonlocal parameter. In addition, the values of field variables (i.e. pressure) in the thickness direction are decreased by increasing the nonlocal parameter for frequencies below 5000 Hz. Furthermore, by increasing the nonlocal parameter, the differences between local and nonlocal values of field variables and the absorption coefficient increase. Also, the nonlocal parameter has no considerable effect on the absorption coefficient for frequencies lower than 2000 Hz, whereas by increasing the nonlocal parameter the differences between corresponding results of local and nonlocal theories increase for frequencies above 2000 Hz.

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