Biot-JKD model: simulation of 1D transient poroelastic waves with fractional derivatives

A time-domain numerical modeling of Biot poroelastic waves is presented. The viscous dissipation occurring in the pores is described using the dynamic permeability model developed by Johnson-Koplik-Dashen (JKD). Some of the coefficients in the Biot-JKD model are proportional to the square root of the frequency: in the time-domain, these coefficients introduce order 1/2 shifted fractional derivatives involving a convolution product. Based on a diffusive representation, the convolution kernel is replaced by a finite number of memory variables that satisfy local-in-time ordinary differential equations. Thanks to the dispersion relation, the coefficients in the diffusive representation are obtained by performing an optimization procedure in the frequency range of interest. A splitting strategy is then applied numerically: the propagative part of Biot-JKD equations is discretized using a fourth-order ADER scheme on a Cartesian grid, whereas the diffusive part is solved exactly. Comparisons with analytical solutions show the efficiency and the accuracy of this approach.Comment: arXiv admin note: substantial text overlap with arXiv:1210.036

Theoretical Simulation of Experimental Observations of Surface Wave Propagation on a Fluid-Saturated Porous Material

Wave propagation in fluid-saturated porous materials presents very particular features like the appearance of a second compressional wave, the so-called slow compressional wave, in addition to the conventional P (or fast compressional) and the shear wave [1,2]. First experimental observation of the slow compressional wave was carried out by Plona in 1980 in water-saturated porous ceramics at ultrasonic frequencies [3]. In 1983 Feng and Johnson predicted the existence of a new surface mode along a fluid/fluid-saturated porous solid interface, in addition to the well-known leaky-Rayleigh and true Stoneley modes [4,5]. Feng and Johnson introduced the so-called surface stiffness, T, as a parameter which describes the boundary conditions at the interface. For a value of T=0 the pores at the surface are considered open, whereas for a value of T=∞ they are considered to be closed. However, according to the theory this new surface mode appears only when closed pores boundary conditions prevail at the interface. This last restriction renders the observation of the new mode problematic, because the extreme difficult in closing the surface pores without clogging all the pores close to the surface (e.g. by painting). In 1992 Nagy observed experimental evidence of the slow surface wave [6]. Nagy demonstrated that capillary forces can extend an ideally thin membrane over the surface pores at the interface between a porous solid saturated with a wetting fluid (e.g. water or alcohol) and a non-wetting fluid (e.g. air). Under this conditions, experimental evidence of a simple form of the new surface wave mode predicted by Feng and Johnson during alcohol saturation of a sintered glass beads specimen was obtained. However, due to problems inherent to the excitation of surface waves in fluid-saturated porous solids (e.g. extremely high attenuation, small propagation lengths, etc.) the results were not conclusive. In this work we will show that the experimental evidence of slow surface wave can be predicted by the analytical method of Feng and Johnson [5], if slight modifications are introduced into the calculation technique in order to account for some of the particular characteristics of the experiment

Surface Wave Inspection of Porous Ceramics and Rocks

The most interesting feature of acoustic wave propagation in fluid-saturated porous media is the appearance of a second compressional wave, the so-called slow compressional wave, in addition to the conventional P (or fast) wave and the shear wave [1,2]. The slow compressional wave is essentially the motion of the fluid along the tortuous paths in the porous frame. This motion is strongly affected by viscous coupling between the fluid and the solid. Therefore, both the velocity and the attenuation of the slow wave greatly depend on the dynamic permeability of the porous frame. It was not until 1980, that Plona first experimentally observed the slow compressional wave in water-saturated porous ceramics at ultrasonic frequencies [3]. Only three years later, Feng and Johnson predicted the existence of a new slow surface mode on a fluid/fluid-saturated solid interface in addition to the well-known leaky-Rayleigh and true Stoneley modes [4,5]. The slow surface mode is basically the interface wave equivalent of the slow bulk mode, but there is a catch: the surface pores of the solid have to be closed so that this new mode can be observed. Otherwise, a surface vibration can propagate along the fluid/fluid-saturated porous solid interface without really moving the fluid since it can flow through the open pores without producing any significant reaction force. All previous efforts directed at the experimental observation of this new surface mode failed because of the extreme difficulty of closing the surface pores without closing all the pores close to the surface (e. g., by painting). On the other hand, it has been recently shown that surface tension itself could be sufficient to produce essentially closed-pore boundary conditions at the interface between a porous solid saturated with a wetting fluid, such as water or alcohol, and a non-wetting superstrate fluid, like air [6]

Downhole well log and core montages from the Mount Elbert Gas Hydrate Stratigraphic Test Well, Alaska North Slope

This paper is not subject to U.S. copyright. The definitive version was published in Marine and Petroleum Geology 28 (2011): 561-577, doi:10.1016/j.marpetgeo.2010.03.016.The BPXA-DOE-USGS Mount Elbert Gas Hydrate Stratigraphic Test Well was an integral part of an ongoing project to determine the future energy resource potential of gas hydrates on the Alaska North Slope. As part of this effort, the Mount Elbert well included an advanced downhole geophysical logging program. Because gas hydrate is unstable at ground surface pressure and temperature conditions, a major emphasis was placed on the downhole-logging program to determine the occurrence of gas hydrates and the in-situ physical properties of the sediments. In support of this effort, well-log and core data montages have been compiled which include downhole log and core-data obtained from the gas-hydrate-bearing sedimentary section in the Mount Elbert well. Also shown are numerous reservoir parameters, including gas-hydrate saturation and sediment porosity log traces calculated from available downhole well log and core data

On Nonspecular Reflection of Bounded Beams for Layered Half Spaces Under Water

We study the recently derived reflection coefficient for plane waves in a liquid that are incident on the liquid-solid interface of a solid half space which consists of a single layer of one elastic material bonded to a substrate of a different material. Plots of the magnitude of the reflection coefficient versus the incident angle are presented for several sets of material parameters and values of frequency f and layer thickness d. The use of the results presented for the study of nonspecular reflection of bounded acoustic beams is of primary interest. We therefore seek to identify all the critical incidence angles for nonspecular reflection. We also investigate, in particular, the surface wave propagation for the case of a stiff layer on a soft half space, and we find that the purely propagating mode cuts off with increasing fd (f is the frequency and d the layer thickness) when its speed reaches approximately the shear wave speed of the substrate, as reported in the literature. However, as fd increases further, a leaky mode appears that approaches the Rayleigh wave for the layer. This leaky mode is also associated with nonspecular reflection for large enough fd.</p

Time domain numerical modeling of wave propagation in 2D heterogeneous porous media

This paper deals with the numerical modeling of wave propagation in porous media described by Biot's theory. The viscous efforts between the fluid and the elastic skeleton are assumed to be a linear function of the relative velocity, which is valid in the low-frequency range. The coexistence of propagating fast compressional wave and shear wave, and of a diffusive slow compressional wave, makes numerical modeling tricky. To avoid restrictions on the time step, the Biot's system is splitted into two parts: the propagative part is discretized by a fourth-order ADER scheme, while the diffusive part is solved analytically. Near the material interfaces, a space-time mesh refinement is implemented to capture the small spatial scales related to the slow compressional wave. The jump conditions along the interfaces are discretized by an immersed interface method. Numerical experiments and comparisons with exact solutions confirm the accuracy of the numerical modeling. The efficiency of the approach is illustrated by simulations of multiple scattering.Comment: Journal of Computational Physics (March 2011

Generalized Lamb Modes in Fluid-Saturated Porous Plate

Since analysis by Rayleigh [1] and Lamb [2], the vibration modes for an elastic homogeneous infinite solid thin plate are well understood. These so-called “Lamb modes” result from a pure compressional wave and pure shear wave. Similarly, excitation of “leaky Lamb modes” in elastic plates immersed in a fluid, caused by incident acoustic waves, has been extensively described theoretically [3–7] and experimentally [8,9]. Results are generally presented as dispersion curves which relate the phase velocity of the mode to the product of frequency and plate thickness

Spory o wysokość stypendium doktoranckiego w okresie wygaszania studiów doktoranckich

Autorka artykułu podejmuje próbę analizy rozbieżności interpretacyjnych art. 285 ustawy z 3 lipca 2018 roku. Przepisy wprowadzające ustawę Prawo o szkolnictwie wyższym i nauce, który to artykuł jest podstawą przyznania stypendium doktoranckiego dla doktorantów wygaszanych studiów trzeciego stopnia. Spory powstałe na gruncie tego przepisu dotyczą wysokości przyznania tego stypendium i podzieliły zarówno środowisko organów przyznających stypendium doktoranckie, jak i jurydykaturę. Wątpliwości budzi określenie podstawy ustalenia wysokości stypendium doktoranckiego dla osób kończących kształcenie na studiach doktoranckich. Część składów orzekających uważa, że wysokość stypendium pozostała zamrożona w stałej wysokości i powinna wynosić 1470 zł. W opozycji jest stanowisko, które przedstawia zwaloryzowaną kwotę stypendium (1923 zł) ustaloną w odniesieniu do aktualnego wynagrodzenia zasadniczego asystenta. Autorka przedstawia analizę argumentacji obu stron i próbę ich oceny