Shear wave dispersion and attenuation in periodic systems of alternating solid and viscous fluid layers

The attenuation and dispersion of elastic waves in fluid-saturated rocks due to the viscosity of the pore fluid is investigated using an idealized exactly solvable example of a system of alternating solid and viscous fluid layers. Waves in periodic layered systems at low frequencies are studied using an asymptotic analysis of Rytov's exact dispersion equations. Since the wavelength of shear waves in fluids (viscous skin depth) is much smaller than the wavelength of shear or compressional waves in solids, the presence of viscous fluid layers necessitates the inclusion of higher terms in the long-wavelength asymptotic expansion. This expansion allows for the derivation of explicit analytical expressions for the attenuation and dispersion of shear waves, with the directions of propagation and of particle motion being in the bedding plane. The attenuation (dispersion) is controlled by the parameter which represents the ratio of Biot's characteristic frequency to the viscoelastic characteristic frequency. If Biot's characteristic frequency is small compared with the viscoelastic characteristic frequency, the solution is identical to that derived from an anisotropic version of the Frenkel-Biot theory of poroelasticity. In the opposite case when Biot's characteristic frequency is greater than the viscoelastic characteristic frequency, the attenuation/dispersion is dominated by the classical viscoelastic absorption due to the shear stiffening effect of the viscous fluid layers. The product of these two characteristic frequencies is equal to the squared resonant frequency of the layered system, times a dimensionless proportionality constant of the order 1. This explains why the visco-elastic and poroelastic mechanisms are usually treated separately in the context of macroscopic (effective medium) theories, as these theories imply that frequency is small compared to the resonant (scattering) frequency of individual pores

Pore scale numerical modeling of elastic wave dispersion and attenuation in periodic systems of alternating solid and viscous fluid layers

Numerical pore-scale simulation of elastic wave propagation is an emerging tool in the analysis of static and dynamic elastic properties of porous materials. Rotated staggered-grid (RSG) finite difference method has proved to be particularly effective in modeling porous media saturated with ideal fluids. Recently this method has been extended to viscoelastic (Maxwell) media, which allows simulation of wave propagation in porous solids saturated with Newtonian fluids. To evaluate the capability of the viscoelastic RSG algorithm in modeling wave dispersion and attenuation we perform numerical simulations for an idealized porous medium, namely a periodic system of alternating solid and viscous fluid layers. Simulations are performed for a single frequency of 50 kHz (for shear waves) and 500 kHz (for compressional waves) and a large range of fluid viscosities. The simulation results show excellent agreement with the theoretical predictions.Specifically the simulations agree with the prediction of Biot's theory of poroelasticity at lower viscosities and with the viscoelastic dissipation at higher viscosities. The finite-difference discretization is required to be sufficiently fine for the appropriate sampling of the viscous boundary layer to achieve accurate simulations at the low values of viscosity. This is an additional accuracy condition for finite-difference simulations in viscoelastic media. 2006 Acoustical Society of America

Comparative review of theoretical models for elastic wave attenuation and dispersion in partially saturated rocks

Saturation of porous rocks with a mixture of two fluids (known as partial saturation) has a substantial effect on the seismic waves propagating through these rocks. In particular, partial saturation causes significant attenuation and dispersion of the propagating waves, due to wave-induced fluid flow. Such flow arises when a passing wave induces different fluid pressures in regions of rock saturated by different fluids. As partial fluid saturation can occur on different length scales, attenuation due to wave induced fluid flow is ubiquitous. In particular, mesoscopic fluid flow due to heterogeneities occurring on a scale greater than porescale, but less than wavelength scale, is responsible for significant attenuation in the frequency range from 10 to 1000 Hz.Most models of attenuation and dispersion due to mesoscopic heterogeneities imply that fluid heterogeneities are distributed in a periodic/regular way. In 1D this corresponds to periodically alternating layering, in 3D as periodically distributed inclusions of a given shape (usually spheres). All these models yield very similar estimates of attenuation and dispersion.Experimental studies show that mesoscopic heterogeneities have less idealised distributions and that the distribution itself affects attenuation and dispersion. Therefore, theoretical models are required which would simulate the effect of more general and realistic fluid distributions.We have developed two theoretical models which simulate the effect of random distributions of mesoscopic fluid heterogeneities. The first model assumes that one fluid forms a random ensemble of spherical inclusions in a porous medium saturated by the other fluid. The attenuation and dispersion predicted by this model are very similar to those predicted for 3D periodic distribution. Attenuation (inverse quality factor) is proportional to at low frequencies for both distributions. This is in contrast to the 1D case, where random and periodically alternating layering shows different attenuation behaviour at low frequencies. The second model, which assumes a 3D continuous distribution of fluid heterogeneities, also predicts the same low-frequency asymptote of attenuation. However, the shapes of the frequency dependencies of attenuation are different. As the 3D continuous random approach assumes that there will be a distribution of different patch sizes, it is expected to be better suited to modelling experimental results. Further research is required in order to uncover how to relate the random functions to experimentally significant parameters

Slow compressional wave in porous media: Finite difference simulations on micro-scale

We perform wave propagation simulations in porous media on microscale in which a slow compressional wave can be observed. Since the theory of dynamic poroelasticity was developed by Biot (1956), the existence of the type II or Biot's slow compressional wave (SCW) remains the most controversial of its predictions. However, this prediction was confirmed experimentally in ultrasonic experiments. The purpose of this paper is to observe the SCW by applying a recently developed viscoelastic displacement-stress rotated staggered finite-difference (FD) grid technique to solve the elastodynamic wave equation. To our knowledge this is the first time that the slow compressional wave is simulated on first principles

Temperature-dependent poroelastic and viscoelastic effects on microscale—modelling of seismic reflections in heavy oil reservoirs

We develop a new model for elastic properties of rocks saturated with heavy oil. The heavy oil is represented by a viscoelastic material, which at low frequencies and/or high temperatures behaves as a Newtonian fluid, and at high frequencies and/or low temperatures as a nearly elastic solid. The bulk and shear moduli of a porous rock saturated with such viscoelastic material are then computed using approximate extended Gassmann equations of Ciz and Shapiro by replacing the elastic moduli of the pore filling material with complex and frequency-dependent moduli of the viscoelastic pore fill. We test the proposed model by comparing its predictions with numerical simulations based on a direct finite-difference solution of equations of dynamic viscoelasticity. The simulations are performed for the reflection coefficient from an interface between a homogeneous fluid and a porous medium. The numerical tests are performed both for an idealized porous medium consisting of alternating solid and viscoelastic layers, and for a more realistic 3-D geometry of the pore space. Both sets of numerical tests show a good agreement between the predictions of the proposed viscoelastic workflow and numerical simulations for relatively high viscosities where viscoelastic effects are important. The results confirm that application of extended Gassmann equations in conjunction with the complex and frequency-dependent moduli of viscoelastic pore filling material, such as heavy oil, provides a good approximation for the elastic moduli of rocks saturated with such material. By construction, this approximation is exactly consistent with the classical Gassmann's equation for sufficiently low frequencies or high temperature when heavy oil behaves like a fluid. For higher frequencies and/or lower temperatures, the predictions are in good agreement with the direct numerical solution of equations of dynamic viscoelasticity on the microscale. This demonstrates that the proposed methodology provides realistic estimates of elastic properties of heavy oil rock

Finite element modelling of the effective elastic properties of partially saturated rocks

Simulation of effective physical properties from microtomographic 3D images of porous structures allows one to relate properties of rocks directly to their microstructure. A static FEM code has been previously used to estimate effective elastic properties of fully saturated monomineralic (quartz) rock under wet and dry conditions. We use the code to calculate elastic properties under partially saturated conditions. The numerical predictions are compared to the Gassmann theory combined with Wood's formula (GW) for a mixture of pore fluids, which is exact for a monomineralic macroscopically homogeneous porous medium. Results of the numerical simulations performed for two Boolean sphere pack distributions show significant deviation from the GW limit and depend on the spatial distribution of fluids. This is shown to be a numerical artefact caused by incomplete equilibration of fluid pressure, which is primarily due to insufficient spatial resolution. To investigate the effect of pore-size and pore geometry, we perform FEM simulations for a model with regular pore geometry, where all pore channels have the same size and shape. Accuracy of these simulations increases with the total cross-section area of the channels and the size of individual channels. For the case where the total cross-section of the channels is large enough (on the same order as total porosity), there is a minimum of 4 voxels per channel diameter required for adequate fluid pressure equilibration throughout the pore space. Increasing the spatial resolution of the digital models reduces the discrepancy between the simulations and theory, but unfortunately increases the memory and CPU requirements of the simulations

A hybrid next generation transcript sequencing-based approach to identify allelic and homeolog-specific single nucleotide polymorphisms in allotetraploid white clover

peer-reviewedBackground: White clover (Trifolium repens L.) is an allotetraploid species possessing two highly collinear ancestral sub-genomes. The apparent existence of highly similar homeolog copies for the majority of genes in white clover is problematic for the development of genome-based resources in the species. This is especially true for the development of genetic markers based on single nucleotide polymorphisms (SNPs), since it is difficult to distinguish between homeolog-specific and allelic variants. Robust methods for categorising single nucleotide variants as allelic or homeolog-specific in large transcript datasets are required. We illustrate one potential approach in this study. Results: We used 454-pyrosequencing sequencing to generate ~760,000 transcript sequences from an 8th generation white clover inbred line. These were assembled and partially annotated to yield a reference transcript set comprising 71,545 sequences. We subsequently performed Illumina sequencing on three further white clover samples, generating 14 million transcript reads from a mixed sample comprising 24 divergent white clover genotypes, and 50 million reads on two further eighth generation white clover inbred lines. Mapping these reads to the reference transcript set allowed us to develop a significant SNP resource for white clover, and to partition the SNPs from the inbred lines into categories reflecting allelic or homeolog-specific variation. The potential for using haplotype reconstruction and progenitor genome comparison to assign haplotypes to specific ancestral sub-genomes of white clover is demonstrated for sequences corresponding to genes encoding dehydration responsive element binding protein and acyl-coA oxidase. Conclusions: In total, 208,854 independent SNPs in 31,715 reference sequences were discovered, approximately three quarters of which were categorised as representing allelic or homeolog-specific variation using two inbred lines. This represents a significant resource for white clover genomics and genetics studies. We discuss the potential to extend the analysis to identify a “core set” of ancestrally derived homeolog specific variants in white clover.Department of Agriculture Food & the Marine, Ireland - Research Stimulus Fund (RSF 07–566

Flavonoids Inhibit the Respiratory Burst of Neutrophils in Mammals

Neutrophils represent the front-line defence cells in protecting organisms against infection and play an irreplaceable role in the proper performance of the immune system. As early as within the first minutes of stimulation, neutrophilic NADPH oxidase is activated, and cells release large quantities of highly toxic reactive oxygen species (ROS). These oxidants can be highly toxic not only for infectious agents but also for neighboring host tissues. Since flavonoids exhibit antioxidant and anti-inflammatory effects, they are subjects of interest for pharmacological modulation of ROS production. The present paper summarizes contemporary knowledge on the effects of various flavonoids on the respiratory burst of mammalian neutrophils. It can be summarized that the inhibitory effects of flavonoids on the respiratory burst of phagocytes are mediated via inhibition of enzymes involved in cell signaling as well as via modulation of redox status. However, the effects of flavonoids are even more complex, and several sites of action, depending upon the flavonoid structure and way of application, are included