Mixture Theories for Rock Properties
01 Mar 2013-pp 205-228
About: The article was published on 2013-03-01. It has received 411 citations till now.
Citations
More filters
Book•
01 Jan 2011TL;DR: In this article, the authors present basic tools for elasticity and Hooke's law, effective media, granular media, flow and diffusion, and fluid effects on wave propagation for wave propagation.
Abstract: Preface 1. Basic tools 2. Elasticity and Hooke's law 3. Seismic wave propagation 4. Effective media 5. Granular media 6. Fluid effects on wave propagation 7. Empirical relations 8. Flow and diffusion 9. Electrical properties Appendices.
2,007 citations
Book•
01 Feb 2005TL;DR: In this paper, the authors present a statistical rock physics approach combining rock physics, information theory, and statistics to reduce uncertainty in seismic data. But they do not discuss the use of statistical methods for quantitative seismic interpretation.
Abstract: Preface 1. Introduction to rock physics 2. Rock physics interpretation of texture, lithology and compaction 3. Statistical rock physics: combining rock physics, information theory, and statistics to reduce uncertainty 4. Common techniques for quantitative seismic interpretation 5. Case studies: lithology and pore-fluid prediction from seismic data 6. Workflows and guide lines 7. Hands-on References Index.
677 citations
TL;DR: In this article, a general Bayesian formulation for the inverse problem can be implemented in two different work flows, in the sequential approach and in the simultaneous work flow, where the elastic parameters and the reservoir properties are assumed to be consistent.
Abstract: There are various approaches for quantitative estimation of reservoir properties from seismic inversion. A general Bayesian formulation for the inverse problem can be implemented in two different work flows. In the sequential approach, first seismic data are inverted, deterministically or stochastically, into elastic properties; then rock-physics models transform those elastic properties to the reservoir property of interest. The joint or simultaneous work flow accounts for the elastic parameters and the reservoir properties, often in a Bayesian formulation, guaranteeing consistency between the elastic and reservoir properties. Rock physics plays the important role of linking elastic parameters such as impedances and velocities to reservoir properties of interest such as lithologies, porosity, and pore fluids. Geostatistical methods help add constraints of spatial correlation, conditioning to different kinds of data and incorporating subseismic scales of heterogeneities.
367 citations
TL;DR: In this paper, the physical properties of gas hydrate-bearing sediments depend on the volume fraction and spatial distribution of the hydrate phase, and the host sediment grain size and the state of effective stress determine hydrate morphology in sediments.
Abstract: [1] The physical properties of gas hydrate-bearing sediments depend on the volume fraction and spatial distribution of the hydrate phase. The host sediment grain size and the state of effective stress determine the hydrate morphology in sediments; this information can be used to significantly constrain estimates of the physical properties of hydrate-bearing sediments, including the coarse-grained sands subjected to high effective stress that are of interest as potential energy resources. Reported data and physical analyses suggest hydrate-bearing sands contain a heterogeneous, patchy hydrate distribution, whereby zones with 100% pore-space hydrate saturation are embedded in hydrate-free sand. Accounting for patchy rather than homogeneous hydrate distribution yields more tightly constrained estimates of physical properties in hydrate-bearing sands and captures observed physical-property dependencies on hydrate saturation. For example, numerical modeling results of sands with patchy saturation agree with experimental observation, showing a transition in stiffness starting near the series bound at low hydrate saturations but moving toward the parallel bound at high hydrate saturations. The hydrate-patch size itself impacts the physical properties of hydrate-bearing sediments; for example, at constant hydrate saturation, we find that conductivity (electrical, hydraulic and thermal) increases as the number of hydrate-saturated patches increases. This increase reflects the larger number of conductive flow paths that exist in specimens with many small hydrate-saturated patches in comparison to specimens in which a few large hydrate saturated patches can block flow over a significant cross-section of the specimen.
237 citations
TL;DR: In this article, the authors generalize Biot's theory of poroelasticity to incorporate wave propagation effects and show how effects that are usually attributed to squirt flow under partially saturated conditions can be explained alternatively in terms of the double-porosity model.
222 citations
References
More filters
Book•
01 Jan 1972
TL;DR: In this paper, the Milieux poreux Reference Record was created on 2004-09-07, modified on 2016-08-08 and the reference record was updated in 2016.
Abstract: Keywords: Ecoulement souterrain ; Milieux poreux Reference Record created on 2004-09-07, modified on 2016-08-08
12,446 citations
"Mixture Theories for Rock Propertie..." refers background in this paper
...General references on uid ow through porous media are Bear [4], Dullien [33], and Adler [1]....
[...]
...Bear, J., Dynamics of Fluids in Porous Media, 764 pp., Elsevier, New York, 1972.5....
[...]
...A key di erence is the no-slip boundary condition for uid ow through porous media.20 General references on uid ow through porous media are Bear [4], Dullien [33], and Adler [1].7.1....
[...]
TL;DR: In this paper, it is shown that to answer several questions of physical or engineering interest, it is necessary to know only the relatively simple elastic field inside the ellipsoid.
Abstract: It is supposed that a region within an isotropic elastic solid undergoes a spontaneous change of form which, if the surrounding material were absent, would be some prescribed homogeneous deformation. Because of the presence of the surrounding material stresses will be present both inside and outside the region. The resulting elastic field may be found very simply with the help of a sequence of imaginary cutting, straining and welding operations. In particular, if the region is an ellipsoid the strain inside it is uniform and may be expressed in terms of tabulated elliptic integrals. In this case a further problem may be solved. An ellipsoidal region in an infinite medium has elastic constants different from those of the rest of the material; how does the presence of this inhomogeneity disturb an applied stress-field uniform at large distances? It is shown that to answer several questions of physical or engineering interest it is necessary to know only the relatively simple elastic field inside the ellipsoid.
11,784 citations
01 May 1952
TL;DR: The connection between the elastic behavior of an aggregate and a single crystal is considered in this article, with special reference to the theories of Voigt, Reuss, and Huber and Schmid.
Abstract: The connection between the elastic behaviour of an aggregate and a single crystal is considered, with special reference to the theories of Voigt, Reuss, and Huber and Schmid. The elastic limit under various stress systems is also considered, in particular, it is shown that the tensile elastic limit of a face-centred aggregate cannot exceed two-thirds of the stress at which pronounced plastic distortion occurs.
7,944 citations
"Mixture Theories for Rock Propertie..." refers background or methods in this paper
...Hill, R., Elastic properties of reinforced solids: Some theoretical principles, J. Mech....
[...]
...For example, the Voigt [98] and Reuss [80] estimates were shown to be rigorous bounds by Hill [46] using variational principles....
[...]
...Hill [46] has shown that the Voigt and Reuss averages are upper and lower bounds on the moduli....
[...]
...For example, the Voigt [98] and Reuss [80] estimateswere shown to be rigorous bounds by Hill [46] using variational principles....
[...]
...Hill, R., A self-consistent mechanics of composite materials, J. Mech....
[...]
TL;DR: In this article, a theory for the propagation of stress waves in a porous elastic solid containing compressible viscous fluid is developed for the lower frequency range where the assumption of Poiseuille flow is valid.
Abstract: A theory is developed for the propagation of stress waves in a porous elastic solid containing compressible viscous fluid. The emphasis of the present treatment is on materials where fluid and solid are of comparable densities as for instance in the case of water‐saturated rock. The paper denoted here as Part I is restricted to the lower frequency range where the assumption of Poiseuille flow is valid. The extension to the higher frequencies will be treated in Part II. It is found that the material may be described by four nondimensional parameters and a characteristic frequency. There are two dilatational waves and one rotational wave. The physical interpretation of the result is clarified by treating first the case where the fluid is frictionless. The case of a material containing viscous fluid is then developed and discussed numerically. Phase velocity dispersion curves and attenuation coefficients for the three types of waves are plotted as a function of the frequency for various combinations of the characteristic parameters.
7,172 citations
TL;DR: In this article, the Berechnung der dielektrizitatatkonstanten and der Leitfahigkeiten fur Elektriatitat and Warme der Mischkorper aus isotropen Bestandteilen behandelt.
Abstract: Es werden verschiedene physikalische Konstanten heterogener Korper aus den Konstanten ihrer homogenen Bestandteile nach einer einheitlichen Methode berechnet. In dieser ersten Arbeit wird die Berechnung der Dielektrizitatskonstanten und der Leitfahigkeiten fur Elektrizitat und Warme der Mischkorper aus isotropen Bestandteilen behandelt. Die Genauigkeit der alteren Formeln wird untersucht und die bis jetzt unbekannten Konstanten dieser Formeln werden berechnet. Sodann wird die Theorie gepruft an Messungen der Leitfahigkeit bei heterogenen Metallegierungen und an den DK. von gepresten Pulvern und Emulsionen; die verschiedenen Formeln werden bestatigt. Bei dieser Anwendung werden einige Widerspruche zwischen fruheren Untersuchungen aufgehoben und es wird versucht, einige ungenau bekannte DK. genauer zu bestimmen.
7,155 citations