Artículos de revistas: "Biot Theory"

1

Stoll, Robert D. "Geoacoustic modeling using the Biot theory". Journal of the Acoustical Society of America 100, n.º 4 (octubre de 1996): 2764. http://dx.doi.org/10.1121/1.416366.

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2

Chotiros, Nicholas P. "Ocean sediments and the Biot theory". Journal of the Acoustical Society of America 144, n.º 3 (septiembre de 2018): 1980. http://dx.doi.org/10.1121/1.5068645.

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3

Ogushwitz, P. R. "Applicability of the Biot theory. II. Suspensions". Journal of the Acoustical Society of America 77, n.º 2 (febrero de 1985): 441–52. http://dx.doi.org/10.1121/1.391864.

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4

Mörig, R. y H. Burkhardt. "Experimental evidence for the Biot‐Gardner theory". GEOPHYSICS 54, n.º 4 (abril de 1989): 524–27. http://dx.doi.org/10.1190/1.1442679.

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Seismic wave attenuation has been a subject of interest during the last 40 years because it may be of use in interpreting seismic data. From this attenuation parameter, more detailed information about the lithology of the subsurface may be deduced if we understand the absorption mechanisms by which dissipation of seismic energy is governed. We are, therefore, studying in the laboratory the effects of different parameters such as porosity, permeability, pore fluid, and saturation state on the absorption of seismic waves in porous rocks over a wide spectrum ranging from seismic to ultrasonic frequencies (Burkhardt et al., 1986).

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5

Katsube, N. "The Constitutive Theory for Fluid-Filled Porous Materials". Journal of Applied Mechanics 52, n.º 1 (1 de marzo de 1985): 185–89. http://dx.doi.org/10.1115/1.3168992.

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The static constitutive theory for fluid-filled porous materials, well established by Biot, is reinvestigated by modifying the recent developments of the micromechanical approach by Carroll. Introducing a new kinematical quantity that allows an equal treatment of fluid and solid, we show that the constitutive theory by Carroll is identical to that developed by Biot. This comparison provides a further insight into Biot’s theory by clarifying the distinct deformation mechanisms that Biot did not express explicitly. Applying the same methods to the dynamic case, we investigate the fluid flow mechanism of a porous fluid material.

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6

Li, Guangquan, Kui Liu y Xiang Li. "Comparison of Fluid Pressure Wave between Biot Theory and Storativity Equation". Geofluids 2020 (26 de octubre de 2020): 1–8. http://dx.doi.org/10.1155/2020/8820296.

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Compressibilities of pore fluid and rock skeleton affect pressure profile and flow velocity of fluid in aquifers. Storativity equation is often used to characterize such effects. The equation suffers from a disadvantage that at infinite large frequency, the predicted velocity of fluid pressure wave is infinitely large, which is unrealistic because any physical processes need certain amounts of time. In this paper, Biot theory is employed to investigate the problem. It is shown that the key equations of Biot theory can be simplified to storativity equation, based on low-frequency assumption. Using Berea sandstone as an example, we compare phase velocity and the quality factor between Biot theory and storativity equation. The results reveal that Biot theory is more accurate in yielding a bounded wave velocity. At frequency lower than 100 kHz, Biot theory yields a wave velocity 8 percent higher than storativity equation does. Apparent permeability measured by fluid pressure wave (such as Oscillatory Hydraulic Tomography) may be 14 percent higher than real permeability measured by steady flow experiments. If skeleton is rigid, Biot theory at very high frequencies or with very high permeabilities will yield the same velocity as sound wave in pure water. The findings help us for better understanding of the physical processes of pore fluid and the limitations of storativity equation.

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7

Nathwani, K. Miguel y Frank S. Henyey. "A modification of Biot theory for unconsolidated sediment." Journal of the Acoustical Society of America 99, n.º 4 (abril de 1996): 2474–500. http://dx.doi.org/10.1121/1.415552.

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8

Khashanah, Khaldoun. "A douglis-nirenberg elliptic operator in biot theory". Applicable Analysis 61, n.º 1-2 (junio de 1996): 87–97. http://dx.doi.org/10.1080/00036819608840446.

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9

Wang, Shu Fang y Ming Xin Zheng. "Application of Biot Consolidation Theory to Analyze Land Subsidence". Advanced Materials Research 168-170 (diciembre de 2010): 2615–18. http://dx.doi.org/10.4028/www.scientific.net/amr.168-170.2615.

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Based on the summary of the status of land subsidence research, Biot Consolidation Theory is proposed to analyze the coupling of seepage field caused by precipitation. By use of Biot consolidation two-dimensional plane finite element calculation programmed, the land subsidence of the WenZhou Yongqiang plain caused by the exploitation of underground water was analyzed. The results are more in line with the measured data, so the method for analysis of possible land subsidence is practicable.

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10

Mikelić, Andro y Mary F. Wheeler. "Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system". Journal of Mathematical Physics 53, n.º 12 (diciembre de 2012): 123702. http://dx.doi.org/10.1063/1.4764887.

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11

Liu, Xu, Stewart Greenhalgh, Bing Zhou y Mark Greenhalgh. "Effective Biot theory and its generalization to poroviscoelastic models". Geophysical Journal International 212, n.º 2 (24 de octubre de 2017): 1255–73. http://dx.doi.org/10.1093/gji/ggx460.

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12

White, J. E. "Biot‐Gardner theory of extensional waves in porous rods". GEOPHYSICS 51, n.º 3 (marzo de 1986): 742–45. http://dx.doi.org/10.1190/1.1442126.

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Many measurements have been made on fluid‐saturated porous rods executing extensional, flexural, and torsional motion. Measurements for extensional and flexural motion yield a loss parameter for Young's modulus waves [Formula: see text], and the measurement for torsional motion yields [Formula: see text] for shear waves. [Formula: see text] has then been calculated for compressional waves in bulk rock, on the assumption that the fluid‐saturated rock is an isotropic solid. I point out the fallacy of computing [Formula: see text] from these measurements and also urge workers to recognize the losses due to simple fluid viscosity in interpreting their data on extensional waves in rods. By application of published theory, I show that peaks in attenuation of extensional waves are to be expected at frequencies of several hertz to several kilohertz, depending upon rod radius. Computed curves are compared with published measurements on Navajo sandstone saturated with water, ethanol, and n‐decane. In each case, computed peak frequency agrees with published measurements. Shift of the peak frequency with temperature from 4 °C to 25 °C is due to change of viscosity of the saturating fluid (water).

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13

Smith, Eric. "Universal features of all‐orders scattering in Biot theory". Journal of the Acoustical Society of America 107, n.º 5 (mayo de 2000): 2921. http://dx.doi.org/10.1121/1.428887.

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14

Ogushwitz, P. R. "Applicability of the Biot theory. I. Low‐porosity materials". Journal of the Acoustical Society of America 77, n.º 2 (febrero de 1985): 429–40. http://dx.doi.org/10.1121/1.391863.

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15

Liu, Xu y Stewart Greenhalgh. "Frequency-domain FD modeling with an adaptable nearly perfectly matched layer boundary condition for poroviscoelastic waves upscaled from the effective Biot theory". GEOPHYSICS 84, n.º 4 (1 de julio de 2019): WA59—WA70. http://dx.doi.org/10.1190/geo2018-0372.1.

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To approximate seismic wave propagation in double-porosity media, one can use the effective Biot theory, which can explain the high level of attenuation observed at seismic frequencies, but which is unaccounted for with classic Biot theory. The governing equations of the effective Biot theory for homogeneous media with complex frequency dispersion characteristics need to be upscaled and extended to S-waves using a poroviscoelastic approach when simulating heterogeneous porous media. We have applied a frequency-space domain mixed grid finite-difference modeling method for this purpose and computed the wavefields for solid particle velocity, fluid flux, and pore pressure. A homogeneous full space model with a single Cole-Cole relaxation function (fractional Zener model) representing the attenuation mechanism is used to indicate that the numerical solutions match fairly well the analytical waveform solutions of the effective Biot theory for source center frequencies ranging from 25 to 10,000 Hz. The computed pore pressure wavefield for a two-layer example porous model is used to further support our numerical method. This model and a laterally heterogeneous three-layer porous medium model further illustrate the applicability of the procedure and even indicate the presence of the slow Biot wave near the interfaces as a result of mode conversion on reflection and transmission. The nearly perfectly matched layer (NPML) absorbing boundary condition is chosen to truncate the computational grid and avoid reflections from the model edges. We found and proved that the NPML performs identically to the PML for either elastic wave modeling or Biot porous medium wave modeling for 3D and 2D scenarios. Two methods to adjust the maximum damping factor (one for the source center frequency and the other for each frequency component) are suggested to adjust the damping factor function in the NPML condition to ensure its effectiveness for various frequency ranges.

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16

Sahay, Pratap N. "On the Biot slow S-wave". GEOPHYSICS 73, n.º 4 (julio de 2008): N19—N33. http://dx.doi.org/10.1190/1.2938636.

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It is accepted widely that the Biot theory predicts only one shear wave representing the in-phase/unison shear motions of the solid and fluid constituent phases (fast S-wave). The Biot theory also contains a shear mode wherein the two constituent phases essentially undergo out-of-phase shear motions (slow S-wave). From the outset of the development of the Biot framework, the existence of this mode has remained unnoticed because of an oversight in decoupling its system of two coupled equations governing shear processes. Moreover, in the absence of the fluid strain-rate term in the Biot constitutive relation, the velocity of this mode is zero. Once the Biot constitutive relation is corrected for the missing fluid strain-rate term (i.e., fluid viscosity), this mode turns out to be, in the inertial regime, a diffusive process akin to a viscous wave in a Newtonian fluid. In the viscous regime, it degenerates to a process governed by a diffusion equation with a damping term. Although this mode is damped so heavily that it dies off rapidly near its source, overlooking its existence ignores a mechanism to draw energy from seismic waves (fast P- and S-waves) via mode conversion at interfaces and at other material discontinuities and inhomogeneities. To illustrate the consequence of generating this mode at an interface, I examine the case of a horizontally polarized fast S-wave normal incident upon a planar air-water interface in a porous medium. Contrary to the classical Biot framework, which suggests that the incident wave should be transmitted practically unchanged through such an interface, the viscosity-corrected Biot framework predicts a strong, fast S-wave reflection because of the slow S-wave generated at the interface.

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17

Best, Angus I. y Clive McCann. "Seismic attenuation and pore‐fluid viscosity in clay‐rich reservoir sandstones". GEOPHYSICS 60, n.º 5 (septiembre de 1995): 1386–97. http://dx.doi.org/10.1190/1.1443874.

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The frequency dependence of seismic attenuation in a suite of clay‐rich reservoir sandstones was investigated in the laboratory. Compressional‐ and shear‐wave velocities ([Formula: see text] and [Formula: see text]) and quality factors ([Formula: see text] and [Formula: see text]) were measured as functions of pore‐fluid viscosity at an effective pressure of 50 MPa and at an experimental frequency of about 0.8 MHz using the pulse‐echo technique. The experimental viscosity ranged from 0.3 to 1000 centipoise, which gives equivalent frequencies for a water‐saturated sandstone of 2.6 MHz to 780 Hz, assuming a global‐flow loss mechanism. Two types of behavior were observed: high permeability (greater than 100 millidarcies) sandstones tend to show variable [Formula: see text] and [Formula: see text] which are similar in magnitude to those predicted by the Biot theory over the viscosity range 0.3 to about 20 centipoise (equivalent frequency range 2.6 MHz to about 39 kHz); low permeability (less than 50 millidarcies) sandstones tend to show almost constant [Formula: see text] and [Formula: see text] over the experimental viscosity range that are not predicted by the Biot theory. The Biot theory does not predict the observed [Formula: see text] and [Formula: see text] values in the high permeability sandstones for viscosities greater than about 20 centipoise, where the observed [Formula: see text] values are generally much lower than the Biot predicted values. High permeability sandstones show small velocity dispersions with changing pore‐fluid viscosity that are consistent with the Biot theory. Low permeability sandstones show relatively large increases in velocity with increasing viscosity not explained by the Biot theory, which are consistent with a local flow loss mechanism. The results indicate the presence of two dominant loss mechanisms: global flow (at least down to about 39 kHz in water‐saturated rocks) in high permeability sandstones with only small amounts of intrapore clay, and local flow at ultrasonic frequencies in low permeability, clay‐rich sandstones.

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18

Block, Gareth y Nicholas Chotiros. "Coupled electrokinetic‐Biot theory and measurement techniques in sediment acoustics". Journal of the Acoustical Society of America 112, n.º 5 (noviembre de 2002): 2310. http://dx.doi.org/10.1121/1.4779312.

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19

Lee, Myung W. "Biot–Gassmann theory for velocities of gas hydrate‐bearing sediments". GEOPHYSICS 67, n.º 6 (noviembre de 2002): 1711–19. http://dx.doi.org/10.1190/1.1527072.

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Elevated elastic velocities are a distinct physical property of gas hydrate‐bearing sediments. A number of velocity models and equations (e.g., pore‐filling model, cementation model, effective medium theories, weighted equations, and time‐average equations) have been used to describe this effect. In particular, the weighted equation and effective medium theory predict reasonably well the elastic properties of unconsolidated gas hydrate‐bearing sediments. A weakness of the weighted equation is its use of the empirical relationship of the time‐average equation as one element of the equation. One drawback of the effective medium theory is its prediction of unreasonably higher shear‐wave velocity at high porosities, so that the predicted velocity ratio does not agree well with the observed velocity ratio. To overcome these weaknesses, a method is proposed, based on Biot–Gassmann theories and assuming the formation velocity ratio (shear to compressional velocity) of an unconsolidated sediment is related to the velocity ratio of the matrix material of the formation and its porosity. Using the Biot coefficient calculated from either the weighted equation or from the effective medium theory, the proposed method accurately predicts the elastic properties of unconsolidated sediments with or without gas hydrate concentration. This method was applied to the observed velocities at the Mallik 2L‐39 well, Mackenzie Delta, Canada.

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20

Ramírez, Nicolás, Maria Paz Raveau, Osvaldo Ramírez y Christopher Feuillade. "Analysis of a Schroeder diffusor using the Biot–Tolstoy theory." Journal of the Acoustical Society of America 126, n.º 4 (2009): 2287. http://dx.doi.org/10.1121/1.3249373.

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21

CASTAGNÈDE, B. y C. DEPOLLIER. "Numerical results and Biot theory in anisotropic porous/fibrous media". Le Journal de Physique IV 04, n.º C5 (mayo de 1994): C5–183—C5–186. http://dx.doi.org/10.1051/jp4:1994534.

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22

Ciarletta, Michele, Brian Straughan y Vincenzo Tibullo. "Acceleration waves in a nonlinear Biot theory of porous media". International Journal of Non-Linear Mechanics 103 (julio de 2018): 23–26. http://dx.doi.org/10.1016/j.ijnonlinmec.2018.04.005.

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23

Ross, Don. "Game Theory as Mathematics for Biology". Biological Theory 2, n.º 1 (marzo de 2007): 104–7. http://dx.doi.org/10.1162/biot.2007.2.1.104.

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24

Norris, Andrew. "The tube wave as a Biot slow wave". GEOPHYSICS 52, n.º 5 (mayo de 1987): 694–96. http://dx.doi.org/10.1190/1.1442336.

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The tube wave speed in a simple fluid‐filled circular bore reduces to [Formula: see text] as the frequency goes to zero, where [Formula: see text] is the acoustic sound speed in the fluid, [Formula: see text] is the fluid density, [Formula: see text] is the fluid bulk modulus, and μ is the formation shear modulus. Biot (1952) deduced this simple relation by considering the low‐frequency asymptotic expansion of the exact dispersion relation. In 1956, Biot proposed a theory (Biot, 1956a, b) that predicts a new type of compressional bulk wave in fluid‐saturated porous media. This “slow wave” is associated mainly with the motion of pore fluids. It appears that Biot never related this theory to his previous work on the bore problem, although the connection is apparent if the bore is considered as a pore. Typically, the bore radius is about 10 cm, while the relevant acoustic logging frequency is on the order of 1 kHz. With water as the bore fluid, the viscous skin depth is on the order of 100 μm. Therefore, if the bore is to be considered as a pore, the relevant form of Biot’s theory is the limit in which the pore radius is large relative to the viscous skin depth of the fluid. This form is the high‐frequency limit, in which the effects of the fluid viscosity are negligible and the slow‐wave dissipation is relatively low.

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25

Thomsen, Leon. "Biot‐consistent elastic moduli of porous rocks: Low‐frequency limit". GEOPHYSICS 50, n.º 12 (diciembre de 1985): 2797–807. http://dx.doi.org/10.1190/1.1441900.

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The semiphenomenological Biot‐Gassmann (B-G) formulation of the low‐frequency elastic moduli of porous rocks does contain two well‐known predictions: (1) the shear modulus of an unsaturated rock (which is permeated by a compressible fluid, e.g., gas) is identical to that of the same rock saturated with liquid, and (2) the unsaturated bulk modulus differs from the saturated bulk modulus by a defined amount. These predictions are tested by ultrasonic data on a large number of sedimentary rocks and are approximately verified, despite the evident frequency discrepancy. The B-G theory makes only minimal assumptions about the microscopic geometry of the rock; therefore, any model theory which does make such assumptions (e.g., spherical pores) should be a special case of B-G theory. In particular, such model theories should also predict the two relations described above. Standard models for dilute concentrations of spherical pores and/or ellipsoidal cracks do predict these relationships. However, in general, the “Self‐Consistent” (S-C) model (developed to deal with finite concentrations of heterogeneities) violates these predictions and hence is not consistent with the underlying Biot‐Gassmann theory. [The special case of S-C theory, corresponding to pores only (no cracks), is consistent with the B-G model.] A new formulation of the model theory, for finite concentrations of heterogeneities of ideal shape, is developed so as to be explicitly consistent with B-G. This “Biot‐consistent” (B-C) formalism is the first theory truly suitable for modeling most sedimentary rocks at seismic frequencies, in terms of porosity and pore shape.

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26

Callebaut, Werner y Manfred D. Laubichler. "Biocomplexity as a Challenge for Biological Theory". Biological Theory 2, n.º 1 (marzo de 2007): 1–2. http://dx.doi.org/10.1162/biot.2007.2.1.1.

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27

Bracanović, Tomislav. "Building Blocks in Search of a Theory". Biological Theory 2, n.º 4 (diciembre de 2007): 422–24. http://dx.doi.org/10.1162/biot.2007.2.4.422.

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28

Guez, David. "A Bio-Logical Theory of Animal Learning". Biological Theory 4, n.º 2 (junio de 2009): 148–58. http://dx.doi.org/10.1162/biot.2009.4.2.148.

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29

Snyderman, Ralph. "Personalized health care: From theory to practice". Biotechnology Journal 7, n.º 8 (16 de diciembre de 2011): 973–79. http://dx.doi.org/10.1002/biot.201100297.

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30

Pride, Steven R., Eric Tromeur y James G. Berryman. "Biot slow‐wave effects in stratified rock". GEOPHYSICS 67, n.º 1 (enero de 2002): 271–81. http://dx.doi.org/10.1190/1.1451799.

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The transmission of P‐waves through the stratified layers of a sedimentary basin is modeled numerically using Biot theory. The effects on the transmissivity of frequency, angle of incidence, layer thickness, permeability and elastic compliance of the rocks are all considered. Consistent with previous analytical work, it is found that the equilibration of fluid pressure between the fine layers of a sedimentary sequence can produce significant P‐wave attenuation at low frequencies. For this attenuation mechanism to act within the surface‐seismic band (say, 3–300 Hz), we find that there must be layering present at the scale of centimeters to tens of centimeters. If the layering is restricted to layers of roughly 1 m thickness or greater, then for typical sandstone formations, the attenuation caused by the interlayer flow occurs below the seismic band of interest. Such low‐frequency interlayer flow is called Biot slow‐wave diffusion in the context of Biot theory and is likely to be the dominant source of low‐frequency attenuation in a sedimentary basin, even for relatively tight and stiff reservoir rock; however, the effect is enhanced in more compliant materials. At higher frequencies, the generation of slow‐waves at interfaces is also shown to significantly affect the P‐wave scattering so long as the layers are sufficiently thin and sufficiently compliant. This effect on the P‐wave scattering is shown to increase with increasing angle of incidence. Our work is limited to performing numerical experiments, with care given to making realistic estimates of all the material properties required. No attempt is made here to define an equivalent viscoelastic solid that allows for such slow‐wave effects.

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31

Mo, Zhuang, Guochenhao Song y J. Stuart Bolton. "A finite difference approach for predicting acoustic behavior of the poro-elastic particle stacks". INTER-NOISE and NOISE-CON Congress and Conference Proceedings 264, n.º 1 (24 de junio de 2022): 350–61. http://dx.doi.org/10.3397/nc-2022-740.

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The physical properties of particle stacks have been of interest for a long time, and the acoustic properties of such materials have been actively investigated in recent times. Traditional acoustic theories, such as the Biot theory, can serve as a guide for determining the general properties of the stacks, but they do not allow the identification of the differences between the particle stacks and traditional acoustic materials, which are usually modeled as homogeneous continua. Recent research suggests that the Biot theory, combined with depth-dependent stiffness and equivalent density, can be used to model such materials. In this work, a finite difference (FD) scheme based on the Biot theory has been developed based on the idea that the apparent stiffness of the particle stack varies with depth within of the stack. This FD scheme is two-dimensional in cylindrical coordinates with an axisymmetric condition imposed at the axis of the cylinder. This approach is thus suitable for modeling common scenarios in which particle stacks are tested in a cylindrical standing wave tube. The results of several example cases are shown in this paper.

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32

Yamamoto, Tokuo. "Imaging permeability structure within the highly permeable carbonate earth: Inverse theory and experiment". GEOPHYSICS 68, n.º 4 (julio de 2003): 1189–201. http://dx.doi.org/10.1190/1.1598103.

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In most oil reservoir rocks, the squirt flow characteristic frequency (fsq) range of 10–100 kHz is much less than the Biot characteristic frequency (f0) range of 1 MHz–1 GHz. In contrast, carbonate aquifers have very high permeability (10–3000 d) and the two characteristic frequencies are reversed: f0 from 10 Hz to 10 kHz and fsq from 1 MHz to 100 MHz. The principal objective of this paper is to develop a pilot inverse method for robust imaging of the high‐permeability structure within carbonate aquifers. An analytical approximate model called the super‐k model is developed. The super‐k model coincides numerically with the combined Biot and squirt‐flow mechanism model when permeability is higher than 100 md and the frequency is lower than 100 kHz (the super‐k regime). In the super‐k regime, the pore fluid is always relaxed so that the attenuation due to the Biot mechanism is roughly four times larger than that of the Biot model. Also, empirical equations are developed that relate the stiffness and rigidity of the skeletal frame and porosity of limestone to compression and shear wave velocities measured from ultrasonic data. The super‐k model is combined with the empirical elastic equations to derive a robust high permeability inverse model. Use of the super‐k inverse model is illustrated in an acoustic crosswell test section of a limestone aquifer between depths of 300 and 480 m over a horizontal width of 11 m. The acoustically imaged permeability, constructed from 4‐kHz velocity and attenuation tomograms, shows excellent agreement with the permeability data obtained hydraulically from pump tests and packer tests performed at four different depth intervals within the test section. The permeability image reveals that the high permeability channels run fairly randomly within the limestone aquifers.

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33

Enelund, Mikael y Peter Olsson. "TIME DOMAIN FORMULATION OF THE BIOT POROELASTIC THEORY USING FRACTIONAL CALCULUS". IFAC Proceedings Volumes 39, n.º 11 (enero de 2006): 391–96. http://dx.doi.org/10.3182/20060719-3-pt-4902.00066.

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34

Depollier, Claude, Jean F. Allard y Walter Lauriks. "Biot theory and stress–strain equations in porous sound‐absorbing materials". Journal of the Acoustical Society of America 84, n.º 6 (diciembre de 1988): 2277–79. http://dx.doi.org/10.1121/1.397024.

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35

Myntiuk, V. B. "Biot Stress and Strain in Thin-Plate Theory for Large Deformations". Journal of Applied and Industrial Mathematics 12, n.º 3 (julio de 2018): 501–9. http://dx.doi.org/10.1134/s1990478918030109.

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36

Yoon, Young June, Jae-Pil Chung, Chul-Soo Bae y Seog-Young Han. "The speed of sound through trabecular bone predicted by Biot theory". Journal of Biomechanics 45, n.º 4 (febrero de 2012): 716–18. http://dx.doi.org/10.1016/j.jbiomech.2011.12.007.

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37

Tong, L. H., Y. S. Liu, D. X. Geng y S. K. Lai. "Nonlinear wave propagation in porous materials based on the Biot theory". Journal of the Acoustical Society of America 142, n.º 2 (agosto de 2017): 756–70. http://dx.doi.org/10.1121/1.4996439.

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38

Fellah, Zine El Abiddine, Jean Yves Chapelon, Walter Lauriks y Claude Depollier. "Ultrasonic wave propagation in human cancellous bone: Application of Biot theory". Journal of the Acoustical Society of America 116, n.º 4 (octubre de 2004): 2476. http://dx.doi.org/10.1121/1.4808669.

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39

Fellah, Z. E. A., J. Y. Chapelon, S. Berger, W. Lauriks y C. Depollier. "Ultrasonic wave propagation in human cancellous bone: Application of Biot theory". Journal of the Acoustical Society of America 116, n.º 1 (julio de 2004): 61–73. http://dx.doi.org/10.1121/1.1755239.

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40

Zhu, X. y G. A. McMechan. "Numerical simulation of seismic responses of poroelastic reservoirs using Biot theory". GEOPHYSICS 56, n.º 3 (marzo de 1991): 328–39. http://dx.doi.org/10.1190/1.1443047.

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Biot theory proSvides a framework for computing the seismic response of fluid‐saturated reservoirs. Numerical implementation by 2-D finite‐differences allows investigation of the effects of spatial variations in porosity, permeability, and fluid viscosity, on seismic displacements of the solid frame and of the fluids (oil, gas, and/or water) in the reservoir. The porosity primarily influences wave velocities; the viscosity‐to‐permeability ratio primarily influences amplitudes and attenuation. Synthetic crosswell, VSP, and surface survey seismograms for representative reservoir models contain primary and converted reflections from fluid as well as lithologic contacts, and they illustrate the distribution of information available for describing a reservoir.

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41

Zhu, X. y G. A. McMechan. "Numerical simulation of seismic responses of poroelastic reservoirs using Biot theory". International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts 28, n.º 6 (noviembre de 1991): A354. http://dx.doi.org/10.1016/0148-9062(91)91316-j.

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42

de Gelder, Beatrice. "Toward a Biological Theory of Emotional Body Language". Biological Theory 1, n.º 2 (junio de 2006): 130–32. http://dx.doi.org/10.1162/biot.2006.1.2.130.

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43

Müller, Tobias M. y Pratap N. Sahay. "Biot coefficient is distinct from effective pressure coefficient". GEOPHYSICS 81, n.º 4 (julio de 2016): L27—L33. http://dx.doi.org/10.1190/geo2015-0625.1.

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Within the Biot poroelasticity theory, the effective pressure coefficient for the bulk volume of a fluid-saturated rock and the Biot coefficient are one and the same quantity. The effective pressure coefficient for the bulk volume is the change of confining pressure with respect to fluid-pressure changes when the bulk volume is held constant. The Biot coefficient is the fluid volume change induced by bulk volume changes in the drained condition. However, there is experimental evidence showing a difference between these two coefficients, arguably caused by microinhomogeneities, such as microcracks and other compliant pore-scale features. In these circumstances, we advocate using the generalized constitutive pressure equations recently developed by Sahay wherein the effective pressure coefficient and the Biot coefficient enter as distinct quantities. Therein, the difference is attributed to the porosity effective pressure coefficient that serves as a measure for the deviation from the Biot prediction and accounts for microinhomogeneities. We have concluded that these generalized constitutive pressure equations offer a meaningful alternative to model observed rock behavior.

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44

Sahay, Pratap N. "Biot constitutive relation and porosity perturbation equation". GEOPHYSICS 78, n.º 5 (1 de septiembre de 2013): L57—L67. http://dx.doi.org/10.1190/geo2012-0239.1.

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In a porous medium, the porosity perturbation, i.e., the change in porosity, is an integral part of a deformation process. Yet, there is no explicit statement about that in the Biot theory. By linking its constitutive relation to the continuity equations, the tacit assumption about the porosity perturbation in this theory is inferred. The linear dependence of the porosity perturbation on the pressure difference of the two phases is embedded in its constitutive relation. The solid and fluid pressures affect the change in porosity in equal magnitude but in opposite sense. By assuming that the fluid pressure may affect the porosity perturbation to an extent different than that of the solid pressure, the Biot constitutive relation is generalized. This introduces a nondimensional parameter. It could be named the porosity effective pressure coefficient, because the measure of the extent the fluid pressure affects the change in porosity relative to the solid pressure. In the regime in which the fluid pressure affects to a lesser extent, this parameter spans from unity, the state in which fluid resists the change in porosity in equal but opposite manner to solid, to zero, the state in which fluid ultimately ceases to affect the porosity change at all. As this parameter diminishes from unity, the undrained bulk modulus drops from being the Gassmann modulus. Ultimately, it becomes the series combination of the dry frame bulk modulus with the bulk modulus of fluid weighted by the Biot coefficient when the parameter is vanishing. The other regime is the one in which the fluid pressure affects to an extent greater than the solid pressure. Here, the parameter may span from unity to the ratio of bulk modulus of constituent solid mineral to fluid, which is its upper limit. At the upper limit, the undrained bulk modulus is the Voigt average: the upper bound of the modulus of a composite medium.

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45

Pierce, Allan D. "Critique of the Biot Theory of Propagation in Fluid-Saturated Porous Solids". Journal of Theoretical and Computational Acoustics 29, n.º 01 (marzo de 2021): 2130002. http://dx.doi.org/10.1142/s2591728521300026.

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Biot’s theory of porous media is discussed critically, with emphasis on the first 1956 JASA paper that purports to apply for low frequencies. It is pointed out that the use of two and only two displacement fields has a certain arbitrariness, and that models with additional displacement fields are possible. Biot’s expression for the strain-energy per unit volume is justified in part, but it is pointed out that additional terms might be included. The theory in the low-frequency limit is discussed in detail, and the partitioning of the disturbance into three distinct types of fields is discussed. It is shown that there is sufficient latitude in the choice of coefficients in the Biot low-frequency model that the coefficients can be adjusted to fit all the major parameters associated with the three types of disturbances at low frequencies, but it is conjectured that the model will lead to inconsistencies for prediction of minor parameters. Unless measurements of such minor parameters are known from independent experiments, the model cannot be tested quantitatively. The use of the low-frequency Biot model at higher frequencies is discussed, and it is shown that in the high-frequency limit there are always two propagating modes where the displacement fields have zero curl. It is also shown that the model predicts the attenuation at high frequencies to be independent of frequency. The validity of such high-frequency predictions is questioned, and it is argued that the Biot low-frequency model has substantial wide-spread validity at low frequencies.

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46

Gist, Grant A. "Interpreting laboratory velocity measurements in partially gas‐saturated rocks". GEOPHYSICS 59, n.º 7 (julio de 1994): 1100–1109. http://dx.doi.org/10.1190/1.1443666.

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It is an old problem in rock physics that the saturation dependence of high‐frequency laboratory velocities does not match the Biot‐Gassmann theory commonly used to predict the effects of gas on seismic velocities. A new interpretation of laboratory velocity data shows that the saturation dependence is controlled by two previously published high‐frequency acoustic mechanisms: (1) a gas pocket model that describes pressure equilibration between liquid and gas‐saturated regions of the pore space, and (2) local fluid flow, induced by pressure equilibration in pores with different aspect ratios. When these two mechanisms are added to Biot theory, the result describes published velocity versus gas saturation data for a wide range of rock types. These two mechanisms are negligible at the lower frequencies of seismic data, so the saturation dependence of laboratory velocities cannot be used to predict the saturation dependence at seismic frequencies. The one laboratory measurement that is relevant for predicting the seismic velocity is the ultrasonic velocity of the dry rock. The dry‐rock velocities should be used in the Biot‐Gassmann theory to predict the full saturation dependence of the seismic velocities.

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Hu, Gang, Haiming Zhao y Zelin Li. "Study on Sound Velocity and Attenuation of Underwater Cobalt-Rich Crust Based on Biot and BISQ Theories". Journal of Marine Science and Engineering 10, n.º 12 (3 de diciembre de 2022): 1880. http://dx.doi.org/10.3390/jmse10121880.

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A prediction model of the sound velocity and sound attenuation of underwater cobalt-rich crusts (CRCs) was established to solve the problem that it is difficult to predict the sound velocity in thickness measurements of cobalt-rich crusts. Based on Biot theory and BISQ theory, a simplified Biot and BISQ model was proposed for the prediction of the sound velocity and sound attenuation of CRCs by using the Kozeny–Carman (KC) equation. The models could calculate the sound velocity and attenuation by the porosity and detection frequency. Based on the physical and mechanical properties of CRCs, a similarity model of the sound velocity and sound attenuation of CRCs was made by using the similarity theory to solve the problem that it is difficult to measure the acoustic propagation characteristics of CRCs. The sound velocity and sound attenuation of CRC similarity models with different porosities were measured by an underwater transmission experiment and the results of the simplified model calculation and experimental measurements were compared. The results showed that the simplified Biot model was suitable for the CRC sound velocity prediction and the simplified BISQ model was suitable for the CRC sound attenuation prediction, which had a high prediction accuracy.

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48

Schneider, Thomas D. "Twenty-five Years of Delila and Molecular Information Theory". Biological Theory 1, n.º 3 (septiembre de 2006): 250–60. http://dx.doi.org/10.1162/biot.2006.1.3.250.

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49

Weber, Bruce H. "Fact, Phenomenon, and Theory in the Darwinian Research Tradition". Biological Theory 2, n.º 2 (junio de 2007): 168–78. http://dx.doi.org/10.1162/biot.2007.2.2.168.

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50

Rosales, Alirio. "The Philosophy of Evolutionary Biology in Theory and Practice". Biological Theory 2, n.º 2 (junio de 2007): 205–7. http://dx.doi.org/10.1162/biot.2007.2.2.205.

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