Attenuation and dispersion of compressional waves in fluid‐filled porous rocks with partial gas saturation (White model)—Part II: Results

Geophysics ◽  
1979 ◽  
Vol 44 (11) ◽  
pp. 1789-1805 ◽  
Author(s):  
N. C. Dutta ◽  
H. Odé
Keyword(s):  
Attenuation Coefficient ◽  
Seismic Waves ◽  
Fluid Pressure ◽  
Porous Solids ◽  
Type I ◽  
Approximate Theory ◽  
Type Ii ◽  
Porous Rocks ◽  
Gas Saturation ◽  
Quantitative Results

In this investigation, Biot’s (1962) theory for wave propagation in porous solids is applied to study the velocity and attenuation of compressional seismic waves in partially gas‐saturated porous rocks. The Physical model, proposed by White (1975), is solved rigorously by using Biot’s equations which describe the coupled solid‐fluid motion of a porous medium in a systematic way. The quantitative results presented here are based on the theory described in Dutta and Odé (1979, this issue). We removed several of White’s questioned approximations and examined their effects on the quantitative results. We studied the variation of the attenuation coefficient with frequency, gas saturation, and size of gas inclusions in an otherwise brine‐filled rock. Anomalously large absorption (as large as 8 dB/cycle) at the exploration seismic frequency band is predicted by this model for young, unconsolidated sandstones. For a given size of the gas pockets and their spacing, the attenuation coefficient (in dB/cycle) increases almost linearly with frequency f to a maximum value and then decreases approximately as 1/√f. A sizable velocity dispersion (of the order of 30 percent) is also predicted by this model. A low gas saturation (4–6 percent) is found to yield high absorption and dispersion. An analysis of all of the field variables (stresses and displacements) is presented in terms of Biot’s type I (the classical compressional) wave and type II (the diffusion) wave. It is pointed out that the dissipation of energy in this model is mainly due to the relative fluid flow from the type II wave. From our formulation, many of White’s equations can be derived as suitable approximations, and it is shown that the discontinuity in fluid pressure assumed by White at the gas‐water interface is the discontinuity in the fluid pressure contribution by the type II wave. Our quantitative results are in reasonably good agreement with White’s (1975) approximate theory. However, the phase velocities computed by White’s approximate treatment do not approach the correct zerofrequency limit (Gassmann‐Wood) when compared to the present theory. Most of these disagreements disappear if the corrections to White’s theory as suggested by Dutta and Seriff (1979, this issue) are incorporated.

On White’s model of attenuation in rocks with partial gas saturation

Geophysics ◽  
1979 ◽  
Vol 44 (11) ◽  
pp. 1806-1812 ◽  
Author(s):  
N. C. Dutta ◽  
A. J. Seriff
Keyword(s):  
Seismic Waves ◽  
Numerical Calculations ◽  
Porous Solids ◽  
Approximate Theory ◽  
Porous Rocks ◽  
Low Frequencies ◽  
Exact Calculations ◽  
Attenuation And Dispersion ◽  
Gas Compressibility ◽  
Good Agreement

In two important papers, J. E. White and coauthors (White, 1975; White et al, 1976) have given an approximate theory for the calculation of attenuation and dispersion of compressional seismic waves in porous rocks filled mostly with brine but containing gas‐filled regions. Modifications of White’s formulas for [Formula: see text] and Q in the case of gas‐filled spheres brings the results into good agreement with the more exact calculations of Dutta and Odé (1979a, b, this issue), who used Biot’s theory for porous solids. In particular, the modified formulas give the expected Gassmann‐Wood velocity at very low frequencies. Inclusion of the finite gas compressibility in numerical calculations for gas‐filled spheres shows an interesting maximum of the attenuation at low gas saturations which is not seen if the gas is ignored. A comparison of the attenuation calculated for the same rock and fluids but for three different geometries of the gas‐filled regions suggests that the configuration of the gas‐filled zones does not have an important effect on the magnitude of the attenuation.

Attenuation and dispersion of compressional waves in fluid‐filled porous rocks with partial gas saturation (White model)—Part I: Biot theory

Geophysics ◽  
1979 ◽  
Vol 44 (11) ◽  
pp. 1777-1788 ◽  
Author(s):  
N. C. Dutta ◽  
H. Odé
Keyword(s):  
Seismic Waves ◽  
Equations Of Motion ◽  
Fluid Pressure ◽  
Present Theory ◽  
Biot Theory ◽  
Type I ◽  
Porous Rocks ◽  
Water Contact ◽  
Coupled Equations ◽  
Attenuation And Dispersion

An exact theory of attenuation and dispersion of seismic waves in porous rocks containing spherical gas pockets (White model) is presented using the coupled equations of motion given by Biot. Assumptions made are (1) the acoustic wavelength is long with respect to the distance between gas pockets and their size, and (2) the gas pockets do not interact. Thus, the present theory essentially is quite similar to that proposed by White (1975), but the problem of the radially oscillating gas pocket is solved in a more rigorous manner by means of Biot’s theory (1962). The solid‐fluid coupling is automatically included, and the model is solved as a boundary value problem requiring all radial stresses and displacements to be continuous at the gas‐brine interface. Thus, we do not require any assumed fluid‐pressure discontinuity at the gas‐water contact, such as the one employed by White (1975). We have also presented an analysis of all of the field variables in terms of Biot’s type I (the classical compressional) wave and, type II (the diffusion) wave. Our quantitative results are presented in Dutta and Odé (1979, this issue).

Equivalent viscoelastic solids for heterogeneous fluid-saturated porous rocks

Geophysics ◽  
2009 ◽  
Vol 74 (1) ◽  
pp. N1-N13 ◽  
Author(s):  
J. Germán Rubino ◽  
Claudia L. Ravazzoli ◽  
Juan E. Santos
Keyword(s):  
Monte Carlo ◽  
Seismic Waves ◽  
Fluid Pressure ◽  
Porous Rocks ◽  
Quality Factors ◽  
Shear Tests ◽  
Viscoelastic Solids ◽  
Shear Moduli ◽  
Phase Velocities ◽  
Biot’S Equations

Different theoretical and laboratory studies on the propagation of elastic waves in real rocks have shown that the presence of heterogeneities larger than the pore size but smaller than the predominant wavelengths (mesoscopic-scale heterogeneities) may produce significant attenuation and velocity dispersion effects on seismic waves. Such phenomena are known as “mesoscopic effects” and are caused by equilibration of wave-induced fluid pressure gradients. We propose a numerical upscaling procedure to obtain equivalent viscoelastic solids for heterogeneous fluid-saturated rocks. It consists in simulating oscillatory compressibility and shear tests in the space-frequency domain, which enable us to obtain the equivalent complex undrained plane wave and shear moduli of the rock sample. We assume that the behavior of the porous media obeys Biot’s equations and use a finite-element procedure to approximate the solutions of the associated boundary value problems. Also, because at mesoscopic scales rock parameter distributions are generally uncertain and of stochastic nature, we propose applying the compressibility and shear tests in a Monte Carlo fashion. This facilitates the definition of average equivalent viscoelastic media by computing the moments of the equivalent phase velocities and inverse quality factors over a set of realizations of stochastic rock parameters described by a given spectral density distribution. We analyzed the sensitivity of the mesoscopic effects to different kinds of heterogeneities in the rock and fluid properties using numerical examples. Also, the application of the Monte Carlo procedure allowed us to determine the statistical properties of phase velocities and inverse quality factors for the particular case of quasi-fractal heterogeneities.

Trapped-Gas Saturations in Carbonate Formations

1975 ◽  
Vol 15 (02) ◽  
pp. 149-160 ◽  
Author(s):  
Dare K. Keelan ◽  
Virgil J. Pugh
Keyword(s):  
Rock Type ◽  
Pore Space ◽  
Gas Storage ◽  
Carbonate Reservoirs ◽  
Type I ◽  
Type Ii ◽  
Gas Saturation ◽  
Porosity And Permeability ◽  
Trapped Gas ◽  
Carbonate Formations

Abstract Trapped-gas saturations existing after gas displacement by wetting-phase imbibition are presented for selected carbonate reservoirs. presented for selected carbonate reservoirs. Formations representing various rock types were investigated, and samples covering the porosity and permeability range within each field were tested. Cores from Smackover reservoirs located within four states were included to examine differences in trapped gas that might occur within a carbonate deposited over a large geographical area. The trapped gas varied with initial gas in place and with rock type. With gas in place of 80 percent of pore space, trapped gas values ranged from a low of 23 percent of pore space in Type II chalk to a maximum of 69 percent in Type I limestone evaluated. Correlation of trapped-gas saturation values was attempted using several approaches, but none was entirely satisfactory. Essentially no relationship with permeability was found within most reservoirs or between different reservoirs. Within a given field, trapped gas at a common initial gas saturation typically increased as porosity decreased. A general interfield correlation with porosity was noted, but certain anomalous data were observed. Knowledge of rock type was necessary to explain these variations in trapped-gas saturations. It was concluded that the complexity of carbonates necessitates determination of trapped gas on the specific reservoir to be evaluated. Introduction Gas reservoirs with a naturally occurring underlying aquifer and aquifer gas storage projects both offer possibilities for large volumes of gas to be trapped and unrecovered. This trapping results from gas-water capillary forces that become active as production occurs and as water encroaches into pore space that previously contained interstitial pore space that previously contained interstitial water and gas. The magnitude of the trapped gas has been reported by others for sandstones, but essentially no information is available in the technical literature for carbonates. A series of carbonate reservoirs was studied to define the magnitude of trapped gas that existed for the range of porosity and permeability found within each reservoir. Trapped-gas saturation values were developed on each core for an initial gas saturation corresponding to irreducible water. Two cores from each reservoir were tested to yield additional trapped saturations for initial gas values of 20 and 50 percent of pore space. These additional data assist in defining trapped gas within a gas-water transition zone or within a gas storage aquifer where considerable variation in gas saturation may exist. Carbonate formations studied were selected to cover a range in pore geometry. Porosity and permeability were not sufficient to classify the permeability were not sufficient to classify the samples or correlate the data. Archie arrived at a classification of carbonate rocks based on the texture of the rock matrix and the nature of the visible pore structure. Table 1 is a summary of the classification, with slight modifications by Jodry. TABLE 1 - ARCHIE ROCK CLASSIFICATION Texture of Appearance of Appearance Under Matrix Hand Sample 10-Power Microscope Type I Crystalline, hard, dense Compact with smooth face on No visible pore space Crystalline breaking. Resinous between crystals Type II Small crystals are less Chalky Dull, earthy, or chalky than 0.05 mm and are earthy with pore space barely visible. Type III Space indicated Granular or Sandy or sugary between crystals or Sucrosic (sucrose) grains. Oolites are in granular class. Matrix Grain Size Symbol Large (coarse) >0.5 mm 1 Medium 0.25 to 0.5 mm m Fine 0.125 to 0.25 mm f Very fine 0.0625 to 0.125 mm vf Extremely fine < 0.0625 mm xf Pore-Size Classification Pore-Size Classification Visible to Visible Diameter Class Naked Eye 10x Magnification (ml) A No No <0.01 B No Yes 0.01 to 0.1 C Yes Yes 0.1 to 1.0 D Yes Yes >1.0 SPEJ P. 149

Heat-Etching with a Bullivant Type II Simple Freeze-Cleave Device

1970 ◽  
Vol 28 ◽  
pp. 106-107 ◽  
Author(s):  
Ronald S. Weinstein ◽  
N. Scott McNutt
Keyword(s):  
New Zealand ◽  
General Hospital ◽  
Massachusetts General Hospital ◽  
Type I ◽  
Type Ii ◽  
Collaborative Effort ◽  
Temperature And Pressure ◽  
The University

The Type I simple cold block device was described by Bullivant and Ames in 1966 and represented the product of the first successful effort to simplify the equipment required to do sophisticated freeze-cleave techniques. Bullivant, Weinstein and Someda described the Type II device which is a modification of the Type I device and was developed as a collaborative effort at the Massachusetts General Hospital and the University of Auckland, New Zealand. The modifications reduced specimen contamination and provided controlled specimen warming for heat-etching of fracture faces. We have now tested the Mass. General Hospital version of the Type II device (called the “Type II-MGH device”) on a wide variety of biological specimens and have established temperature and pressure curves for routine heat-etching with the device.

Labelling of non-A, non-B hepatitis infected chimpanzee hepatocytes with nuclease-gold conjugates

1984 ◽  
Vol 42 ◽  
pp. 250-251
Author(s):  
G. D. Gagne ◽  
M. F. Miller ◽  
D. A. Peterson
Keyword(s):  
Endoplasmic Reticulum ◽  
Experimental Infection ◽  
Uranyl Acetate ◽  
Type I ◽  
Cellular Injury ◽  
Type Ii ◽  
Tubular Structures ◽  
Type Iii ◽  
Type Iv ◽  
Infected Chimpanzee

Experimental infection of chimpanzees with non-A, non-B hepatitis (NANB) or with delta agent hepatitis results in the appearance of characteristic cytoplasmic alterations in the hepatocytes. These alterations include spongelike inclusions (Type I), attached convoluted membranes (Type II), tubular structures (Type III), and microtubular aggregates (Type IV) (Fig. 1). Type I, II and III structures are, by association, believed to be derived from endoplasmic reticulum and may be morphogenetically related. Type IV structures are generally observed free in the cytoplasm but sometimes in the vicinity of type III structures. It is not known whether these structures are somehow involved in the replication and/or assembly of the putative NANB virus or whether they are simply nonspecific responses to cellular injury. When treated with uranyl acetate, type I, II and III structures stain intensely as if they might contain nucleic acids. If these structures do correspond to intermediates in the replication of a virus, one might expect them to contain DNA or RNA and the present study was undertaken to explore this possibility.

Comparative surface and ultrastructural views of methylotrophic bacteria by TEM, STEM, SE, and freeze-etch electron microscopy.

1987 ◽  
Vol 45 ◽  
pp. 792-793
Author(s):  
T.A. Fassel ◽  
M.J. Schaller ◽  
M.E. Lidstrom ◽  
C.C. Remsen
Keyword(s):  
Cytoplasmic Membrane ◽  
Structural Features ◽  
Methylotrophic Bacteria ◽  
Type I ◽  
Type Ii ◽  
Membrane Complex ◽  
Oxidation Of Methane ◽  
Methane Oxidizing Bacteria ◽  
Wall Structures ◽  
Methylomonas Albus

Methylotrophic bacteria play an Important role in the environment in the oxidation of methane and methanol. Extensive intracytoplasmic membranes (ICM) have been associated with the oxidation processes in methylotrophs and chemolithotrophic bacteria. Classification on the basis of ICM arrangement distinguishes 2 types of methylotrophs. Bundles or vesicular stacks of ICM located away from the cytoplasmic membrane and extending into the cytoplasm are present in Type I methylotrophs. In Type II methylotrophs, the ICM form pairs of peripheral membranes located parallel to the cytoplasmic membrane. Complex cell wall structures of tightly packed cup-shaped subunits have been described in strains of marine and freshwater phototrophic sulfur bacteria and several strains of methane oxidizing bacteria. We examined the ultrastructure of the methylotrophs with particular view of the ICM and surface structural features, between representatives of the Type I Methylomonas albus (BG8), and Type II Methylosinus trichosporium (OB-36).

OPTICAL STUDIES OF TYPE I AND TYPE II RECOMBINATION IN GaAs-AlAs QUANTUM WELLS

1987 ◽  
Vol 48 (C5) ◽  
pp. C5-525-C5-528 ◽  
Author(s):  
K. J. MOORE ◽  
P. DAWSON ◽  
C. T. FOXON
Keyword(s):  
Quantum Wells ◽  
Type I ◽  
Type Ii ◽  
Optical Studies
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