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Voigt–Reuss bounds

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Proceedings Papers

Paper presented at the SEG/AAPG/SEPM First International Meeting for Applied Geoscience & Energy, September 26–October 1, 2021
Paper Number: SEG-2021-3594819
... be predicted by attributed to the lack of image resolution to resolve sub- Hashin-Shtrikman or Voigt-Reuss bounds. Our workflow micron scale features, including pore-grain boundaries, yields a range of effective elastic moduli of rocks that bound grain-to-grain contacts, and micro-porous regions. A bias...
Proceedings Papers

Paper presented at the SEG International Exposition and Annual Meeting, September 15–20, 2019
Paper Number: SEG-2019-3215256
... analysis together with the modified Voigt-Reuss bounds, porosity, the rock intrinsically have, determines the variability of the static moduli, which decreases with the increasing porosity. Moreover, the static moduli are highly dependent on the stress path or history. In general, the unloading bulk...
Proceedings Papers

Paper presented at the 2013 SEG Annual Meeting, September 22–27, 2013
Paper Number: SEG-2013-0304
... saturation of carbon dioxide. In this study we use the Voigt-Reuss bounds, also known as the harmonic and arithmetic averages (Mavko et al., 1998) to represent the extreme variation that is possible in relating the saturation of carbon dioxide to seismic compressional velocity. The Voigt upper bound...
Proceedings Papers

Paper presented at the 1995 SEG Annual Meeting, October 8–13, 1995
Paper Number: SEG-1995-0878
... specific velocity estimates. In general, when only the volume fractions of the constituents are known, without additional geometric details of their arrangements, specifying the bound is the best we can do. The best known and simplest bounds are the Voigt (1928), Mv, and Reuss (1929), MR averages, which...
Proceedings Papers

Paper presented at the 2017 SEG International Exposition and Annual Meeting, September 24–29, 2017
Paper Number: SEG-2017-17638364
... properties by the Voigt-Reuss bounds, and then calculate the average values to obtain the elastic properties of the kerogen powder. We analyze the sensitivity of synthetic aggregate method. The spread of the Voigt-Reuss bounds can be written as Where M is elastic modulus, f is volume concentration thus f1+f2...
Proceedings Papers

Paper presented at the 2017 SEG International Exposition and Annual Meeting, September 24–29, 2017
Paper Number: SEG-2017-17558033
... combines two classical methods together. © 2017 SEG SEG International Exposition and 87th Annual Meeting Page 3666 A novel brittleness equation for shale formation based on Voigt-Reuss-Hill average Figure 3 Diagram indicates Voigt and Reuss bound 1 _ * N i i i BI V f RBI (4a) 1 1 _ N i i i f BI R RBI...
Proceedings Papers

Paper presented at the 2018 SEG International Exposition and Annual Meeting, October 14–19, 2018
Paper Number: SEG-2018-2997247
... ABSTRACT The well-known Voigt upper bound and Reuss lower bound are subcategories of weighted power mean with a power parameter of 1 and -1, respectively. The power mean is a monotonic function of the power parameter. Therefore, the elastic properties of a rock can always be modeled...
Proceedings Papers

Paper presented at the 2015 SEG Annual Meeting, October 18–23, 2015
Paper Number: SEG-2015-5883969
... and much stiffer than the initial pore-fill. As outlined for the first substituted composite, we compute the Voigt and Reuss elastic moduli and obtain four sets of embedded bounds for this second substituted composite too. It is interesting to note that for each of the three composites, the Voigt...
Proceedings Papers

Paper presented at the 2017 SEG International Exposition and Annual Meeting, September 24–29, 2017
Paper Number: SEG-2017-17792957
... a classic segmentation model with modifications of the Hashin-Shtrikman upper bound, and modifications of the Voigt-Reuss-Hill bound. The elastic property matrices that we obtain with these effective medium theories are used as models to simulate the propagation of ultrasonic waves. All effective medium...
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Calculated seismic response using different <b>bounds</b> to describe the bulk mod...
Published: 09 October 2017
Figure 3 Calculated seismic response using different bounds to describe the bulk modulus of the pore-filling fluids. (a) Acoustic impedance changes based on the Voigt bound. (b) Acoustic impedance changes based on the Reuss bound. (c) Onset Time based on the Voigt bound, and (d) Onset Time based More
Proceedings Papers

Paper presented at the 2009 SEG Annual Meeting, October 25–30, 2009
Paper Number: SEG-2009-2238
... predictions of S–wave velocity can be made without explicit knowledge of microstructure. Thus, by applying theoretical bounding equations like ReussVoigt and the tighter Hashin–Shtrikman bounds we should be able to theoretically explain empirical predictions for S– waves. A porous rock is a mixture and may...
Proceedings Papers

Paper presented at the 2012 SEG Annual Meeting, November 4–9, 2012
Paper Number: SEG-2012-0554
... (1929) and Voigt (1910) averages were used by White (1975) to define bounds on the velocity-saturation relationship, and the Reuss average is assumed to apply to low frequency scenarios. Domenico (1976) was the first to suggest that the heterogeneity of the fluid distribution in a rock might affect its...
Proceedings Papers

Paper presented at the 2010 SEG Annual Meeting, October 17–22, 2010
Paper Number: SEG-2010-0373
... to predict lithology and pore-fluid. The water depth in this case is about 1200 meters and the target depth of the sands vary between 3000-5000 m TVDss. Rock physics analysis Both the Voigt-Reuss and Hashin-Shtrikman upper and lower bounds were used to assess the elastic moduli of the clean sands from...
Proceedings Papers

Paper presented at the 2013 SEG Annual Meeting, September 22–27, 2013
Paper Number: SEG-2013-1319
... velocities on 9 laboratory isolated kerogen samples from Green River shale in Colorado. From data measured on both dry and saturated samples, we can invert the bulk modulus of kerogen using the Gassmanm equation, Reuss bound and Voigt bound. The bulk modulus of kerogen is estimated to lie around 3.5-5 GPa...
Proceedings Papers

Paper presented at the 2005 SEG Annual Meeting, November 6–11, 2005
Paper Number: SEG-2005-1485
... ABSTRACT When developing rock physics models that make use of contact theories such as Hertz-Mindlin, we need a good estimate of moduli at the point just below critical porosity, where the rock has finite bulk and shear moduli. Voigt and Reuss bound equations can be applied...
Proceedings Papers

Paper presented at the 2005 SEG Annual Meeting, November 6–11, 2005
Paper Number: SEG-2005-1557
... water and finally iv) stiff clay (without absorbed water). Final Voigt Mix Orientation Reuss Q+ADW mix 0 5 10 15 20 25 30 35 0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4 0,45 0,5 Total Porosity (fraction) B u lk M o d u lu s (G P a) RES>6 RES 4-6 RES 2.5-4 RES 1.5-2.5 RES 0.5-1.5 RES 0-0.5 VOIGT Clay Part...
Proceedings Papers

Paper presented at the 2002 SEG Annual Meeting, October 6–11, 2002
Paper Number: SEG-2002-1837
... Summary For isotropic, homogeneous porous materials, Gassmann’s (1951) equations are physically constrained by the Voigt and Reuss bounds and critical porosity. . These bounds provide stricter constraints on input parameters and output results of fluid saturation effects on bulk modulus. We...
Proceedings Papers

Paper presented at the 2016 SEG International Exposition and Annual Meeting, October 16–21, 2016
Paper Number: SEG-2016-13846801
...) and shear (G) moduli obtained by Voigt and Reuss averaging form the widest possible bounds on those moduli and can be neatly summarized in terms of the components of the individual domain stiffness/compliance tensor (Sumino and Anderson, 1984). These are given by Equations. 8-11, Page 398© 2016 SEG SEG...
Proceedings Papers

Paper presented at the International Petroleum Technology Conference, March 26–28, 2013
Paper Number: IPTC-16977-MS
... is performed by using theoretical rock physics models e.g. Voigt-Reuss-Hill model, Hashin-Sthrikman bound model, Kuster-Toksoz model, and Clausius-mossotti model. Consequently, the result brings a wider scientific view of the thin section image which now becomes both geologically and physically meaningfull...
Proceedings Papers

Paper presented at the 2004 SEG Annual Meeting, October 10–15, 2004
Paper Number: SEG-2004-1746
... ABSTRACT There are several methods by which partial gas saturation can be predicted from acoustic impedance results. Here well logs and core are used along with Gassmann Equations, Voigt and Reuss averages for the fluid mixture (corresponding to patchy and homogeneous mixtures respectively...

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