Bounds on low‐frequency seismic velocities in partially saturated rocks

Geophysics ◽  
1998 ◽  
Vol 63 (3) ◽  
pp. 918-924 ◽  
Author(s):  
Gary Mavko ◽  
Tapan Mukerji
Keyword(s):  
Low Frequency ◽  
Pore Fluid ◽  
Rock Properties ◽  
Upper And Lower Bounds ◽  
Small Scale ◽  
Seismic Velocities ◽  
Fluid Properties ◽  
Seismic Frequencies ◽  
The Individual ◽  
Wave Induced

The most common technique for estimating seismic velocities in rocks with mixed pore fluid saturations is to use Gassmann’s relations with an effective fluid whose density and compressibility are averages of the individual pore fluid properties. This approach is applicable only if the gas, oil, and brine phases are mixed uniformly at a very small scale, so the different wave‐induced increments of pore pressure in each phase have time to diffuse and equilibrate during a seismic period. In contrast, saturations that are heterogeneous over scales larger than the characteristic diffusion length, i.e., patchy saturation, will always lead to higher seismic velocities than if the same fluids are mixed uniformly at a fine scale. Critical saturation scales separating uniform from patchy behavior are typically of the order 0.1–1 cm for laboratory measurements and tens of centimeters for field seismic frequencies. For low seismic frequencies, velocities corresponding to patchy and homogeneous saturations represent approximate upper and lower bounds for given saturations and dry rock properties. For well‐consolidated rocks, both bounds can be estimated easily using Gassmann’s relations with Voigt and Reuss average effective fluids, respectively.

Seismic signatures of reservoir transport properties and pore fluid distribution

Geophysics ◽  
1994 ◽  
Vol 59 (8) ◽  
pp. 1222-1236 ◽  
Author(s):  
Nabil Akbar ◽  
Gary Mavko ◽  
Amos Nur ◽  
Jack Dvorkin
Keyword(s):  
Bulk Modulus ◽  
Solid Phase ◽  
Low Frequency ◽  
Pore Fluid ◽  
Fluid Distribution ◽  
Geometrical Factor ◽  
Velocity Versus ◽  
Frequency Limit ◽  
Local Flow ◽  
Wave Induced

We investigate the effects of permeability, frequency, and fluid distribution on the viscoelastic behavior of rock. The viscoelastic response of rock to seismic waves depends on the relative motion of pore fluid with respect to the solid phase. Fluid motion depends, in part, on the internal wave‐induced pore pressure distribution that relates to the pore micro‐structure of rock and the scales of saturation. We consider wave‐induced squirt fluid flow at two scales: (1) local microscopic flow at the smallest scale of saturation heterogeneity (e.g., within a single pore) and (2) macroscopic flow at a larger scale of fluid‐saturated and dry patches. We explore the circumstances under which each of these mechanisms prevails. We examine such flows under the conditions of uniform confining (bulk) compression and obtain the effective dynamic bulk modulus of rock. The solutions are formulated in terms of generalized frequencies that depend on frequency, saturation, fluid and gas properties, and on the macroscopic properties of rock such as permeability, porosity, and dry bulk modulus. The study includes the whole range of saturation and frequency; therefore, we provide the missing link between the low‐frequency limit (Gassmann’s formula) and the high‐frequency limit given by Mavko and Jizba. Further, we compare our model with Biot’s theory and introduce a geometrical factor whose numeric value gives an indication as to whether local fluid squirt or global (squirt and/or Biot’s) mechanisms dominate the viscoelastic properties of porous materials. The important results of our theoretical modeling are: (1) a hysteresis of acoustic velocity versus saturation resulting from variations in fluid distributions, and (2) two peaks of acoustic wave attenuation—one at low frequency (caused by global squirt‐flow) and another at higher frequency (caused by local flow). Both theoretical results are compared with experimental data.

Stuck between a rock and a reflection: A tutorial on low-frequency models for seismic inversion

2017 ◽  
Vol 5 (2) ◽  
pp. B17-B27 ◽  
Author(s):  
Mark Sams ◽  
David Carter
Keyword(s):  
Elastic Properties ◽  
Model Building ◽  
Seismic Velocity ◽  
Low Frequency ◽  
Rock Physics ◽  
Frequency Component ◽  
Seismic Inversion ◽  
Rock Properties ◽  
Seismic Velocities ◽  
Frequency Model

Predicting the low-frequency component to be used for seismic inversion to absolute elastic rock properties is often problematic. The most common technique is to interpolate well data within a structural framework. This workflow is very often not appropriate because it is too dependent on the number and distribution of wells and the interpolation algorithm chosen. The inclusion of seismic velocity information can reduce prediction error, but it more often introduces additional uncertainties because seismic velocities are often unreliable and require conditioning, calibration to wells, and conversion to S-velocity and density. Alternative techniques exist that rely on the information from within the seismic bandwidth to predict the variations below the seismic bandwidth; for example, using an interpretation of relative properties to update the low-frequency model. Such methods can provide improved predictions, especially when constrained by a conceptual geologic model and known rock-physics relationships, but they clearly have limitations. On the other hand, interpretation of relative elastic properties can be equally challenging and therefore interpreters may find themselves stuck — unsure how to interpret relative properties and seemingly unable to construct a useful low-frequency model. There is no immediate solution to this dilemma; however, it is clear that low-frequency models should not be a fixed input to seismic inversion, but low-frequency model building should be considered as a means to interpret relative elastic properties from inversion.

An Innovative Methodology for Estimating Rock Mechanical Properties from Weight or Volume Fractions of Mineralogy and its Application to Middle East Reservoirs

2021 ◽  
Author(s):  
Umesh Prasad ◽  
Amer Hanif ◽  
Ian McGlynn ◽  
Frank Walles ◽  
Ahmed Abouzaid ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Public Domain ◽  
New Method ◽  
Rock Properties ◽  
Upper And Lower Bounds ◽  
Geomechanical Model ◽  
Volume Fractions ◽  
Fluid Properties ◽  
Tight Formations ◽  
Rock Mechanical Properties

Abstract The influences of mineralogy on rock mechanical properties have profound application in oil and gas exploration and production processes, including hydraulic fracturing operations. In conventional resources, the rock mechanical properties are predominantly controlled by porosity; however, in unconventional tight formations, the importance of mineralogy as a function of rock mechanical properties has not been fully investigated. In unconventional tight formations, mechanical properties are often derived from mineralogy weight fraction together with the best estimate of porosity, assumption of fluid types, the extent of pore fillings, and fluid properties. These properties are then adjusted for their volumetric fractions and subsequently calibrated with acoustics or geomechanical lab measurements. A new method is presented that utilizes mineralogy weight fractions (determined from well logs or laboratory measurements). This process uses public domain information of minerals using Voigt and Reuss averaging algorithms as upper and lower bounds, respectively. An average of these bounds (also known as Hill average) provides a representative value for these parameters. Further, based on isotropic conditions, all the elastic properties are calculated. A typical output consisting of bulk-, shear-, and Young's - modulus, together with Poisson's ratio obtained from traditional methods of volume fractions and this new method using weight fractions is discussed and analyzed along with the sensitivity and the trends for individual rock properties. Furthermore, corresponding strengths, hardness, and fracture toughness could also be estimated using well known public domain algorithms. Data from carbonate reservoirs has been discussed in this work. This method shows how to estimate grain compressibility that can be challenging to be measured in the lab for unconventional tight rock samples. In low-porosity samples, the relative influence of porosity is negligible compared to the mineralogy composition. This approach reduces several assumptions and uncertainties associated with accurate porosity determination in tight rocks as it does not require the amount of pore fluids and fluid properties in calculations. The grain-compressibility and bulk-compressibility (measured by hydrostatic tests in the laboratory on core plugs or calculated from density and cross-dipole log) are used to calculate poroelastic Biot's coefficient, as this coefficient will be used to calculate in-situ principal effective stresses (overburden, minimum horizontal, and maximum horizontal stresses), which are, together with rock properties and pore pressure, constitutes the geomechanical model. The geomechanical model is used for drilling, completions, and hydraulic fracture modeling, including wellbore stability, and reservoir integrity analyses.

scholarly journals Exact expression for the effective acoustics of patchy-saturated rocks

Geophysics ◽  
2010 ◽  
Vol 75 (4) ◽  
pp. N87-N96 ◽  
Author(s):  
Bouko Vogelaar ◽  
David Smeulders ◽  
Jerry Harris
Keyword(s):  
Oil And Gas ◽  
Low Frequency ◽  
Exact Expression ◽  
P Wave ◽  
Rock Properties ◽  
Partially Saturated ◽  
P Wave Velocity ◽  
Seismic Frequencies ◽  
Exact Analytic Expression ◽  
Conventional Models

Seismic effects of a partially gas-saturated subsurface have been known for many years. For example, patches of nonuniform saturation occur at the gas-oil and gas-water contacts in hydrocarbon reservoirs. Open-pore boundary conditions are applied to the quasi-static Biot equations of poroelasticity to derive an exact analytic expression of the effective bulk modulus for partially saturated media with spherical gas patches larger than the typical pore size. The pore fluid and the rock properties can have different values in the central sphere and in the surrounding region. An analytic solution prevents loss of accuracy from ill-conditioned equations as encountered in the numerical solution for certain input. For a sandstone saturated with gas and water, we found that the P-wave velocity and attenuation in conventional models differ as much as 15% from the exact solution at seismic frequencies. This makes the use of present exact theory necessary to describe patchy saturation, although (more realistic) complex patch shapes and distributions were not considered. We found that, despite earlier corrections, the White conventional model does not yield the correct low-frequency asymptote for the attenuation.

Macroscopic mechanical properties of porous rock with one saturating fluid

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. MR223-MR239 ◽  
Author(s):  
Wubing Deng ◽  
Igor B. Morozov
Keyword(s):  
Mechanical Properties ◽  
Laboratory Experiments ◽  
Kinetic Equations ◽  
Low Frequency ◽  
Fluid Flows ◽  
Pore Fluid ◽  
P Wave ◽  
Rock Properties ◽  
Porous Rock ◽  
Arbitrary Boundary

Effective frequency-dependent moduli and [Formula: see text]-factors are broadly used for characterizing the behavior of earth media in laboratory and field seismic observations. However, such properties are wavemode- and experiment-dependent and are often incomplete and/or inaccurate for modeling realistic situations. For example, viscoelastic moduli for porous fluid-saturated rock are usually derived for primary waves, but they may not apply to cases in which secondary waves are important, such as reflections in finely layered poroelastic media or quasistatic pore-fluid flows in laboratory experiments. To obtain a model applicable to all cases, equations of mechanics should be used, and mechanical properties of the material must be identified. To reveal and measure such properties for fluid-saturated porous rock, we have developed a Biot-consistent model based on Lagrangian continuum mechanics. The model is “minimal,” purely macroscopic, and independent of the macrostructure or patterns of pore-fluid flows; thus, it could represent many existing wave-induced fluid-flow (WIFF) as well as non-WIFF models. Due to its mechanical definition, the model should be applicable to all rock-physics experiments (linear creep, pore flow, low-frequency, resonant, or ultrasonic), any waves in the field (primary, secondary, standing, surface, etc.) under arbitrary boundary conditions, and also finite-difference and finite-element numerical modeling. When based on this model, numerical simulations require no integral equations, fractional derivatives, memory variables, or additional kinetic equations. We further use the model to invert for detailed elastic and viscous properties of fluid-saturated Berea and Fontainebleau sandstones from recently published low-frequency laboratory experiments. All rock properties inferred in the model are time- and frequency-independent, comparable to other physical observations, and the model closely predicts the data. The model can be approximately pore-fluid independent, which allows performing rigorous fluid substitution with viscous pore fluids. As an illustration, P-wave velocity dispersion and attenuation in water-, oil-, and gas-saturated sandstone are simulated.

Reflecting the Sky in Water

2017 ◽  
Vol 3 (1) ◽  
pp. 112-126 ◽  
Author(s):  
Ilaria Cristofaro
Keyword(s):  
The Unconscious ◽  
Related Case ◽  
Quality Of Water ◽  
Fluid Properties ◽  
Phenomenological Perspective ◽  
Auto Ethnography ◽  
The Individual ◽  
Artificial Water ◽  
Land Water

From a phenomenological perspective, the reflective quality of water has a visually dramatic impact, especially when combined with the light of celestial phenomena. However, the possible presence of water as a means for reflecting the sky is often undervalued when interpreting archaeoastronomical sites. From artificial water spaces, such as ditches, huacas and wells to natural ones such as rivers, lakes and puddles, water spaces add a layer of interacting reflections to landscapes. In the cosmological understanding of skyscapes and waterscapes, a cross-cultural metaphorical association between water spaces and the underworld is often revealed. In this research, water-skyscapes are explored through the practice of auto-ethnography and reflexive phenomenology. The mirroring of the sky in water opens up themes such as the continuity, delimitation and manipulation of sky phenomena on land: water spaces act as a continuation of the sky on earth; depending on water spaces’ spatial extension, selected celestial phenomena can be periodically reflected within architectures, so as to make the heavenly dimension easily accessible and a possible object of manipulation. Water-skyscapes appear as specular worlds, where water spaces are assumed to be doorways to the inner reality of the unconscious. The fluid properties of water have the visual effect of dissipating borders, of merging shapes, and, therefore, of dissolving identities; in the inner landscape, this process may represent symbolic death experiences and rituals of initiation, where the annihilation of the individual allows the creative process of a new life cycle. These contextually generalisable results aim to inspire new perspectives on sky-and-water related case studies and give value to the practice of reflexive phenomenology as crucial method of research.

scholarly journals The VC Dimension of Metric Balls under Fréchet and Hausdorff Distances

2021 ◽  
Author(s):  
Anne Driemel ◽  
André Nusser ◽  
Jeff M. Phillips ◽  
Ioannis Psarros
Keyword(s):  
Density Estimation ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Similarity Metrics ◽  
Vc Dimension ◽  
Set Systems ◽  
Polygonal Curves ◽  
The Individual ◽  
Curve Similarity ◽  
Metric Balls

AbstractThe Vapnik–Chervonenkis dimension provides a notion of complexity for systems of sets. If the VC dimension is small, then knowing this can drastically simplify fundamental computational tasks such as classification, range counting, and density estimation through the use of sampling bounds. We analyze set systems where the ground set X is a set of polygonal curves in $$\mathbb {R}^d$$ R d and the sets $$\mathcal {R}$$ R are metric balls defined by curve similarity metrics, such as the Fréchet distance and the Hausdorff distance, as well as their discrete counterparts. We derive upper and lower bounds on the VC dimension that imply useful sampling bounds in the setting that the number of curves is large, but the complexity of the individual curves is small. Our upper and lower bounds are either near-quadratic or near-linear in the complexity of the curves that define the ranges and they are logarithmic in the complexity of the curves that define the ground set.

scholarly journals 3–D Models of Galaxy Magnetic Fields with Spiral Shocks

1990 ◽  
Vol 140 ◽  
pp. 133-134
Author(s):  
J. Panesar ◽  
A.H. Nelson
Keyword(s):  
Gas Flow ◽  
Density Wave ◽  
Shock Velocity ◽  
Small Scale ◽  
Hydrodynamic Simulation ◽  
Dynamo Equation ◽  
Scale Turbulence ◽  
Wave Induced ◽  
The Magnetic Field ◽  
Stellar Density

We report here some preliminary results of 3–D numerical simulations of an α–ω dynamo in galaxies with differential rotation, small–scale turbulence, and a shock wave induced by a stellar density wave. We obtain the magnetic field from the standard dynamo equation, but include the spiral shock velocity field from a hydrodynamic simulation of the gas flow in a gravitational field with a spiral perturbation (Johns and Nelson, 1986).

Collective oscillations in bubble clouds

2011 ◽  
Vol 680 ◽  
pp. 114-149 ◽  
Author(s):  
ZORANA ZERAVCIC ◽  
DETLEF LOHSE ◽  
WIM VAN SAARLOOS
Keyword(s):  
Frequency Response ◽  
Acoustic Field ◽  
Low Frequency ◽  
Acoustic Energy ◽  
Viscous Damping ◽  
Edge States ◽  
Bubble Cloud ◽  
Collective Oscillations ◽  
The Individual ◽  
Bubble Oscillations

In this paper the collective oscillations of a bubble cloud in an acoustic field are theoretically analysed with concepts and techniques of condensed matter physics. More specifically, we will calculate the eigenmodes and their excitabilities, eigenfrequencies, densities of states, responses, absorption and participation ratios to better understand the collective dynamics of coupled bubbles and address the question of possible localization of acoustic energy in the bubble cloud. The radial oscillations of the individual bubbles in the acoustic field are described by coupled linearized Rayleigh–Plesset equations. We explore the effects of viscous damping, distance between bubbles, polydispersity, geometric disorder, size of the bubbles and size of the cloud. For large enough clusters, the collective response is often very different from that of a typical mode, as the frequency response of each mode is sufficiently wide that many modes are excited when the cloud is driven by ultrasound. The reason is the strong effect of viscosity on the collective mode response, which is surprising, as viscous damping effects are small for single-bubble oscillations in water. Localization of acoustic energy is only found in the case of substantial bubble size polydispersity or geometric disorder. The lack of localization for a weak disorder is traced back to the long-range 1/r interaction potential between the individual bubbles. The results of the present paper are connected to recent experimental observations of collective bubble oscillations in a two-dimensional bubble cloud, where pronounced edge states and a pronounced low-frequency response had been observed, both consistent with the present theoretical findings. Finally, an outlook to future possible experiments is given.

scholarly journals Speech Identification with Temporal and Spectral Modification in Subjects with Auditory Neuropathy

2012 ◽  
Vol 2012 ◽  
pp. 1-7
Author(s):  
Vijaya Kumar Name ◽  
C. S. Vanaja
Keyword(s):  
Signal Processing ◽  
Speech Processing ◽  
Word Identification ◽  
Low Frequency ◽  
Auditory Neuropathy ◽  
Study Word ◽  
Spectral Modification ◽  
The Individual ◽  
High Pass ◽  
Speech Identification

Background. The aim of this study was to investigate the individual effects of envelope enhancement and high-pass filtering (500 Hz) on word identification scores in quiet for individuals with Auditory Neuropathy. Method. Twelve individuals with Auditory Neuropathy (six males and six females) with ages ranging from 12 to 40 years participated in the study. Word identification was assessed using bi-syllabic words in each of three speech processing conditions: unprocessed, envelope-enhanced, and high-pass filtered. All signal processing was carried out using MATLAB-7. Results. Word identification scores showed a mean improvement of 18% with envelope enhanced versus unprocessed speech. No significant improvement was observed with high-pass filtered versus unprocessed speech. Conclusion. These results suggest that the compression/expansion signal processing strategy enhances speech identification scores—at least for mild and moderately impaired individuals with AN. In contrast, simple high-pass filtering (i.e., eliminating the low-frequency content of the signal) does not improve speech perception in quiet for individuals with Auditory Neuropathy.

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