scholarly journals Biot‐consistent elastic moduli of porous rocks: Low‐frequency limit

Geophysics ◽  
1985 ◽  
Vol 50 (12) ◽  
pp. 2797-2807 ◽  
Author(s):  
Leon Thomsen
Keyword(s):  
Bulk Modulus ◽  
Model Theory ◽  
Elastic Moduli ◽  
Sedimentary Rocks ◽  
Low Frequency ◽  
Porous Rocks ◽  
Seismic Frequencies ◽  
New Formulation ◽  
Special Case ◽  
Finite Concentrations

The semiphenomenological Biot‐Gassmann (B-G) formulation of the low‐frequency elastic moduli of porous rocks does contain two well‐known predictions: (1) the shear modulus of an unsaturated rock (which is permeated by a compressible fluid, e.g., gas) is identical to that of the same rock saturated with liquid, and (2) the unsaturated bulk modulus differs from the saturated bulk modulus by a defined amount. These predictions are tested by ultrasonic data on a large number of sedimentary rocks and are approximately verified, despite the evident frequency discrepancy. The B-G theory makes only minimal assumptions about the microscopic geometry of the rock; therefore, any model theory which does make such assumptions (e.g., spherical pores) should be a special case of B-G theory. In particular, such model theories should also predict the two relations described above. Standard models for dilute concentrations of spherical pores and/or ellipsoidal cracks do predict these relationships. However, in general, the “Self‐Consistent” (S-C) model (developed to deal with finite concentrations of heterogeneities) violates these predictions and hence is not consistent with the underlying Biot‐Gassmann theory. [The special case of S-C theory, corresponding to pores only (no cracks), is consistent with the B-G model.] A new formulation of the model theory, for finite concentrations of heterogeneities of ideal shape, is developed so as to be explicitly consistent with B-G. This “Biot‐consistent” (B-C) formalism is the first theory truly suitable for modeling most sedimentary rocks at seismic frequencies, in terms of porosity and pore shape.

To: “Biot‐consistent elastic moduli of porous rocks: Low‐frequency limit,” by Leon Thomsen which appeared on p. 2797–2807 in December 1985 GEOPHYSICS:

Geophysics ◽  
1986 ◽  
Vol 51 (4) ◽  
pp. 1033-1033
Keyword(s):  
Elastic Moduli ◽  
Low Frequency ◽  
Porous Rocks ◽  
Frequency Limit ◽  
Text Page

The following typesetting errors have been noted in the article: Page 2802: equation (8) should read equation (9); ϕ should read [Formula: see text] in equation (13). Budiansky and O’Connell (1977) should read O’Connell and Budiansky (1977). 1˜6v* should read [Formula: see text]*, 1˜6v should read [Formula: see text]. Page 2803: 1˜6τ should read [Formula: see text], 1¯6θ should read [Formula: see text], [ + should read [1 + in equation (16b), 1¯6γ should read [Formula: see text]. Page 2804: [Formula: see text] should read [Formula: see text] in equations (17b), (17d). 1¯6τ should read [Formula: see text], 1¯6γ should read [Formula: see text], ϕ should read [Formula: see text] in equation (19), [Formula: see text] should read [Formula: see text] in step (9), [Formula: see text] should read [Formula: see text]

scholarly journals Laboratory measurements of low- and high-frequency elastic moduli in Fontainebleau sandstone

Geophysics ◽  
2013 ◽  
Vol 78 (5) ◽  
pp. D369-D379 ◽  
Author(s):  
Emmanuel C. David ◽  
Jérome Fortin ◽  
Alexandre Schubnel ◽  
Yves Guéguen ◽  
Robert W. Zimmerman
Keyword(s):  
Bulk Modulus ◽  
Elastic Moduli ◽  
High Pressures ◽  
Low Frequency ◽  
Frequency Dispersion ◽  
Low Frequencies ◽  
High Frequencies ◽  
Fontainebleau Sandstone ◽  
Wave Velocities ◽  
Water Saturated

The presence of pores and cracks in rocks causes the fluid-saturated wave velocities in rocks to be dependent on frequency. New measurements of the bulk modulus at low frequencies (0.02–0.1 Hz) were obtained in the laboratory using oscillation tests carried out on two hydrostatically stressed Fontainebleau sandstone samples, in conjunction with ultrasonic velocities and static measurements, under a range of differential pressures (10–95 MPa), and with three different pore fluids (argon, glycerin, and water). For the 13% and 4% porosity samples, under glycerin- and water-saturated conditions, the low-frequency bulk modulus at 0.02 Hz matched well the low-frequency and ultrasonic dry bulk modulus. The glycerin- and water-saturated samples were much more compliant at low frequencies than at high frequencies. The measured bulk moduli of the tested rocks at low frequencies (0.02–0.1 Hz) were much lower than the values predicted by the Gassmann equation. The frequency dispersion of the P and S velocities was much higher at low differential pressures than at high pressures, due to the presence of open cracks at low differential pressures.

Influence of the Creep Effect on the Low-Frequency Measurements of the Elastic Moduli of Sedimentary Rocks

2019 ◽  
Author(s):  
R. Chavez ◽  
V. Mikhaltsevitch ◽  
M. Lebedev ◽  
B. Gurevich ◽  
E. Vargas ◽  
...  
Keyword(s):  
Elastic Moduli ◽  
Sedimentary Rocks ◽  
Low Frequency ◽  
Frequency Measurements ◽  
Creep Effect

Estimation of porosity, fluid bulk modulus, and stiff-pore volume fraction using a multi-trace Bayesian AVO petrophysics inversion in multi-porosity reservoirs

Geophysics ◽  
2021 ◽  
pp. 1-101
Author(s):  
Kun Li ◽  
Xingyao Yin ◽  
Zhaoyun Zong ◽  
Dario Grana
Keyword(s):  
Bulk Modulus ◽  
Pore Volume ◽  
Elastic Moduli ◽  
Wave Reflection ◽  
Volume Fraction ◽  
Inversion Method ◽  
Reservoir Properties ◽  
Pore Volume Fraction ◽  
Pp Wave ◽  
Matrix Shear

The estimation of petrophysical and fluid-filling properties of subsurface reservoirs from seismic data is a crucial component of reservoir characterization. Seismic amplitude variation with offset (AVO) inversion driven by rock physics is an effective approach to characterize reservoir properties. Generally, PP-wave reflection coefficients, elastic moduli and petrophysical parameters are nonlinearly coupled, especially in the multiple type pore-space reservoirs, which makes seismic AVO petrophysics inversion ill-posed. We propose a new approach that combines Biot-Gassmann’s poro-elasticity theory with Russell’s linear AVO approximation, to estimate the reservoir properties including elastic moduli and petrophysical parameters based on multi-trace probabilistic AVO inversion algorithm. We first derive a novel PP-wave reflection coefficient formulation in terms of porosity, stiff-pore volume fraction, rock matrix shear modulus, and fluid bulk modulus to incorporate the effect of pore structures on elastic moduli by considering the soft and stiff pores with different aspect ratios in sandstone reservoirs. Through the analysis of the four types of PP-wave reflection coefficients, the approximation accuracy and inversion feasibility of the derived formulation are verified. The proposed stochastic inversion method aims to predict the posterior probability density function in a Bayesian setting according to a prior Laplace distribution with vertical correlation and prior Gaussian distribution with lateral correlation of model parameters. A Metropolis-Hastings stochastic sampling algorithm with multiple Markov chains is developed to simulate the posterior models of porosity, stiff-pore volume fraction, rock-matrix shear modulus, and fluid bulk modulus from seismic AVO gathers. The applicability and validity of the proposed inversion method is illustrated with synthetic examples and a real data application.

scholarly journals Extremely small twist elastic constants in lyotropic nematic liquid crystals

2020 ◽  
Vol 117 (44) ◽  
pp. 27238-27244 ◽  
Author(s):  
Clarissa F. Dietrich ◽  
Peter J. Collings ◽  
Thomas Sottmann ◽  
Per Rudquist ◽  
Frank Giesselmann
Keyword(s):  
Liquid Crystals ◽  
Elastic Constant ◽  
Elastic Constants ◽  
Nematic Phase ◽  
Elastic Moduli ◽  
Building Blocks ◽  
Lyotropic Liquid Crystals ◽  
Order Of Magnitude ◽  
Typical Range ◽  
Special Case

Recent measurements of the elastic constants in lyotropic chromonic liquid crystals (LCLCs) have revealed an anomalously small twist elastic constant compared to the splay and bend constants. Interestingly, measurements of the elastic constants in the micellar lyotropic liquid crystals (LLCs) that are formed by surfactants, by far the most ubiquitous and studied class of LLCs, are extremely rare and report only the ratios of elastic constants and do not include the twist elastic constant. By means of light scattering, this study presents absolute values of the elastic constants and their corresponding viscosities for the nematic phase of a standard LLC composed of disk-shaped micelles. Very different elastic moduli are found. While the splay elastic constant is in the typical range of 1.5 pN as is true in general for thermotropic nematics, the twist elastic constant is found to be one order of magnitude smaller (0.30 pN) and almost two orders of magnitude smaller than the bend elastic constant (21 pN). These results demonstrate that a small twist elastic constant is not restricted to the special case of LCLCs, but is true for LLCs in general. The reason for this extremely small twist elastic constant very likely originates with the flexibility of the assemblies that are the building blocks of both micellar and chromonic lyotropic liquid crystals.

Lunar rock Q in 3000-5000 range achieved in laboratory

1977 ◽  
Vol 285 (1327) ◽  
pp. 475-479 ◽  
Keyword(s):  
Seismic Data ◽  
Room Temperature ◽  
Low Frequency ◽  
Thin Layers ◽  
Lunar Sample ◽  
Lunar Rock ◽  
Seismic Frequencies ◽  
Different Gases ◽  
Frequency Apparatus

Q measurements carried out by the vibrating bar technique on lunar sample 70215,85 have yielded Q values as high as 4800 at room temperature. The strong outgassing procedures necessary to raise the Q to these high values from Q =- 60 (when received) and studies of the effect on Q by a variety of different gases shows that the removal of thin layers of adsorbed H 2 O are responsible for the dramatic increase in Q . Experiments carried out with a low frequency apparatus on a terrestrial analogue at 50 Hz suggest similar increases in Q with outgassing, thus providing evidence that dramatic effects on Q can be expected to occur down to seismic frequencies. These results, in part, explain the contrast between seismic data in the lunar and terrestrial crust in terms of the absence and presence respectively of adsorbed H 2 O.

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