An inclusion‐based model of elastic wave velocities incorporating patch‐scale fluid pressure relaxation

Geophysics ◽  
2003 ◽  
Vol 68 (5) ◽  
pp. 1503-1509 ◽  
Author(s):  
S. Richard Taylor ◽  
Rosemary J. Knight
Keyword(s):  
Elastic Wave ◽  
Elastic Moduli ◽  
Effective Medium Theory ◽  
Fluid Pressure ◽  
P Wave ◽  
Pore Fluids ◽  
Wave Velocities ◽  
Wave Cycle ◽  
Dependent Flow ◽  
Patch Scale

We consider elastic wave velocities in fluid‐saturated porous media with pore fluids distributed in “patches” (i.e., heterogeneity much larger than the typical pore size). We model elastic properties of such materials using inclusion‐based effective medium theory (IBEMT). The standard IBEMT formulation assumes insufficient time during the wave cycle for pore fluids to flow in response to wave‐induced pressure gradients. Our approach accounts for this flow, incorporating wave‐frequency dependent flow effects in the definition of effective elastic moduli for patches. Effective moduli are used in conjunction with IBEMT to estimate elastic moduli of the composite material. In the low‐ and high‐frequency limits, the model reproduces previous theoretical results. At intermediate frequencies, it yields results qualitatively similar to other patch‐scale models. We demonstrate this approach, estimating elastic P‐wave velocities and attenuation in a porous rock that simultaneously contains fluid‐saturated patches of different sizes.

Incorporating mechanisms of fluid pressure relaxation into inclusion‐based models of elastic wave velocities

Geophysics ◽  
2003 ◽  
Vol 68 (4) ◽  
pp. 1173-1181 ◽  
Author(s):  
S. Richard Taylor ◽  
Rosemary J. Knight
Keyword(s):  
Elastic Wave ◽  
Water Saturation ◽  
Laboratory Data ◽  
Fluid Pressure ◽  
P Wave ◽  
Porous Rocks ◽  
Low Frequencies ◽  
Wave Velocities ◽  
Exact Agreement ◽  
Flow Through

Our new method incorporates fluid pressure communication into inclusion‐based models of elastic wave velocities in porous rocks by defining effective elastic moduli for fluid‐filled inclusions. We illustrate this approach with two models: (1) flow between nearest‐neighbor pairs of inclusions and (2) flow through a network of inclusions that communicates fluid pressure throughout a rock sample. In both models, we assume that pore pressure gradients induce laminar flow through narrow ducts, and we give expressions for the effective bulk moduli of inclusions. We compute P‐wave velocities and attenuation in a model sandstone and illustrate that the dependence on frequency and water‐saturation agrees qualitatively with laboratory data. We consider levels of water saturation from 0 to 100% and all wavelengths much larger than the scale of material heterogeneity, obtaining near‐exact agreement with Gassmann theory at low frequencies and exact agreement with inclusion‐based models at high frequencies.

Effective elastic properties of rocks with transversely isotropic background permeated by a set of vertical fracture cluster

Geophysics ◽  
2021 ◽  
pp. 1-78
Author(s):  
Da Shuai ◽  
Alexey Stovas ◽  
Jianxin Wei ◽  
Bangrang Di ◽  
Yang Zhao
Keyword(s):  
Standard Deviation ◽  
Elastic Wave ◽  
Significant Influence ◽  
Transversely Isotropic ◽  
Azimuth Angle ◽  
Effective Medium ◽  
P Wave ◽  
Wave Velocities ◽  
Anisotropy Parameters ◽  
Vertical Fractures

The linear slip theory is gradually being used to characterize seismic anisotropy. If the transversely isotropic medium embeds vertical fractures (VFTI medium), the effective medium becomes orthorhombic. The vertical fractures, in reality, may exist in any azimuth angle which leads the effective medium to be monoclinic. We apply the linear slip theory to create a monoclinic medium by only introducing three more physical meaning parameters: the fracture preferred azimuth angle, the fracture azimuth angle, and the angular standard deviation. First, we summarize the effective compliance of a rock as the sum of the background matrix compliance and the fracture excess compliance. Then, we apply the Bond transformation to rotate the fractures to be azimuth dependent, introduce a Gaussian function to describe the fractures' azimuth distribution assuming that the fractures are statistically distributed around the preferred azimuth angle, and average each fracture excess compliance over azimuth. The numerical examples investigate the influence of the fracture azimuth distribution domain and angular standard deviation on the effective stiffness coefficients, elastic wave velocities, and anisotropy parameters. Our results show that the fracture cluster parameters have a significant influence on the elastic wave velocities. The fracture azimuth distribution domain and angular standard deviation have a bigger influence on the orthorhombic anisotropy parameters in the ( x2, x3) plane than that in the ( x1, x3) plane. The fracture azimuth distribution domain and angular standard deviation have little influence on the monoclinic anisotropy parameters responsible for the P-wave NMO ellipse and have a significant influence on the monoclinic anisotropy parameters responsible for the S1- and S2-wave NMO ellipse. The effective monoclinic can be degenerated into the VFTI medium.

The influence of pore fluids and frequency on apparent effective stress behavior of seismic velocities

Geophysics ◽  
2010 ◽  
Vol 75 (1) ◽  
pp. N1-N7 ◽  
Author(s):  
Gary Mavko ◽  
Tiziana Vanorio
Keyword(s):  
Elastic Wave ◽  
Bulk Modulus ◽  
Effective Stress ◽  
High Frequency ◽  
Laboratory Data ◽  
Pore Fluids ◽  
Wave Velocities ◽  
Stress Behavior ◽  
Stress Coefficient ◽  
The Impact

Although poroelastic theory predicts that the effective stress coefficient equals unity for elastic moduli in monomineralic rocks, some rock elastic wave velocities measured at ultrasonic frequencies have effective stress coefficients less than one. Laboratory effective stress behavior for P-waves is often different than S-waves. Furthermore, laboratory ultrasonic velocities almost always reflect high-frequency artifacts associated with pore fluids, including an increase in velocities and flattening of velocity-versus-pressure curves. We have investigated the impact of pore fluids and frequency on the observed effective stress coefficient for elastic wave velocities by developing a model that calculates pore-fluid effects on velocity, including high-frequency squirt dispersion, and we have compared the model’s predictions with laboratory data. We modeled a rock frame with penny-shaped cracks for three situations: vacuum dry, saturated with helium, and saturated with brine. Even if the frame modulus depends only on the differential stress, the saturated-rock effective stress coefficient is predicted to be significantly less than one at ultrasonic frequencies because of two effects: an increase in the fluid bulk modulus with increasing pressure and the contribution of high-frequency squirt dispersion. The latter effect is most significant in soft fluids (helium in this experiment) in which the fluid-bulk modulus is less than or comparable to the thin-crack pore stiffness.

TOTAL POROSITY AND MATRIX PARAMETERS OF CARBONATE ROCKS BASED ON THE ELASTIC WAVE VELOCITY AND DENSITY MEASUREMENTS

2018 ◽  
Vol 473 (473) ◽  
pp. 13-26
Author(s):  
Jadwiga JARZYNA ◽  
Edyta PUSKARCZYK ◽  
Ewa OGÓREK ◽  
Jacek MOTYKA
Keyword(s):  
Elastic Wave ◽  
Elastic Waves ◽  
Total Porosity ◽  
Elastic Wave Velocity ◽  
P Wave ◽  
Reservoir Properties ◽  
Rock Samples ◽  
Additional Information ◽  
Wave Velocities ◽  
Boundary Velocity

The purpose of the research was to find relationship between elastic waves velocities obtained from lab measurements and parameters from hydrogeological research. Measurements were conducted on 73 rock samples originating mostly from Jurassic limestone of the Olkusz area. Additional information about the rock samples was obtained when the elastic wave velocities were compared with reservoir parameters such as porosity, permeability and density. Plots of elastic waves velocities vs. porosity and bulk density vs. porosity gave information about the range of P wave velocities from the boundary velocity to the values when porosity is equal to zero. Matrix velocity and density values were introduced into the formulas used to calculate porosity. Anisotropy analysis was made on the basis of elastic wave velocities measured on cores cut in two perpendicular directions. This allowed for identification of fractures in rocks. Results showed that by comparing various petrophysical parameters it was possible to get better information about reservoir properties of aquifers.

scholarly journals Relationships between Dynamic Elastic Moduli in Shale Reservoirs

Energies ◽  
2020 ◽  
Vol 13 (22) ◽  
pp. 6001
Author(s):  
Sheyore John Omovie ◽  
John P. Castagna
Keyword(s):  
Organic Carbon ◽  
Shear Modulus ◽  
Elastic Moduli ◽  
Volume Fraction ◽  
P Wave ◽  
Wave Velocities ◽  
Shear Wave Velocities ◽  
Average Formation ◽  
Dynamic Elastic Moduli ◽  
Shale Reservoirs

Sonic log compressional and shear-wave velocities combined with logged bulk density can be used to calculate dynamic elastic moduli in organic shale reservoirs. We use linear multivariate regression to investigate modulus prediction when shear-wave velocities are not available in seven unconventional shale reservoirs. Using only P-wave modulus derived from logged compressional-wave velocity and density as a predictor of dynamic shear modulus in a single bivariate regression equation for all seven shale reservoirs results in prediction standard error of less than 1 GPa. By incorporating compositional variables in addition to P-wave modulus in the regression, the prediction standard error is reduced to less than 0.8 GPa with a single equation for all formations. Relationships between formation bulk and shear moduli are less well defined. Regressing against formation composition only, we find the two most important variables in predicting average formation moduli to be fractional volume of organic matter and volume of clay in that order. While average formation bulk modulus is found to be linearly related to volume fraction of total organic carbon, shear modulus is better predicted using the square of the volume fraction of total organic carbon. Both Young’s modulus and Poisson’s ratio decrease with increasing TOC while increasing clay volume decreases Young’s modulus and increases Poisson’s ratio.

Comparison of seismic upscaling methods: From sonic to seismic

Geophysics ◽  
2009 ◽  
Vol 74 (2) ◽  
pp. WA3-WA14 ◽  
Author(s):  
Dileep K. Tiwary ◽  
Irina O. Bayuk ◽  
Alexander A. Vikhorev ◽  
Evgeni M. Chesnokov
Keyword(s):  
Elastic Wave ◽  
Pair Correlation ◽  
P Wave ◽  
Frequency Bandwidth ◽  
Frequency Range ◽  
S Wave ◽  
Wave Velocities ◽  
Backus Averaging ◽  
The Difference ◽  
Gas Bearing

The term “upscaling” used here means a prediction of elastic-wave velocities at lower frequencies from the velocities at higher frequencies. Three different methods of upscaling are considered, including the simple averaging, Backus averaging, and pair correlation function methods. These methods are applied to upscale the elastic-wave velocities measured at sonic frequencies ([Formula: see text], logging data) available for a well penetrating layers of gas-bearing shales and carbonates. As a result, a velocity distribution over depth for [Formula: see text] and [Formula: see text] is found in the frequency range of [Formula: see text]. The difference in the results obtained for a particular depth by the three theoretical methods in the surface seismic frequency bandwidth [Formula: see text] is [Formula: see text] for P-wave and [Formula: see text] for S-wave velocity. This difference is attributed to different theoretical backgrounds underlying these methods.

scholarly journals On three-stage temperature dependence of elastic wave velocities for rocks

2021 ◽  
Vol 18 (3) ◽  
pp. 328-338
Author(s):  
Nianqi Li ◽  
Li-Yun Fu ◽  
Jian Yang ◽  
Tongcheng Han
Keyword(s):  
Elastic Wave ◽  
Temperature Dependence ◽  
Elastic Constants ◽  
Nonlinear Behavior ◽  
P Wave ◽  
Shape Model ◽  
Wave Velocities ◽  
Nonlinear Thermoelasticity ◽  
Velocity Variations ◽  
Shape Curve

Abstract For most rocks, the typical temperature behavior of elastic wave velocities generally features a three-stage nonlinear characteristic that could be expressed by a reverse S-shape curve with two inflexion points. The mechanism regulating the slow-to-fast transition of elastic constants remains elusive. The physics of critical points seems related to the multimineral composition of rocks with differentiated thermodynamic properties. Based on laboratory experiments for several rocks with different levels of heterogeneity in compositions, we conduct theoretical and empirical simulations by nonlinear thermoelasticity methods and a S-shape model, respectively. The classical theory of linear thermoelasticity based on the Taylor expansion of strain energy functions has been widely used for crystals, but suffers from a deficiency in describing thermal-associated velocity variations for rocks as a polycrystal mixture. Current nonlinear thermoelasticity theory describes the third-order temperature dependence of velocity variations by incorporating the fourth-order elastic constants. It improves the description of temperature-induced three-stage velocity variations in rocks, but involves with some divergences around two inflexion points, especially at high temperatures. The S-shape model for empirical simulations demonstrates a more accurate depiction of thermal-associated three-stage variations of P-wave velocities. We investigate the physics of the parameters ${a_1}$ and ${b_1}$ in the S-shape model. These fitting parameters are closely related to thermophysical properties by being proportional to the specific heat and thermal conductivity of rocks. We discuss the mechanism that regulates the slow-to-fast transition in the three-stage nonlinear behavior for various rocks.

scholarly journals Effect of pore fluid pressure on elastic wave velocities of serpentinites

2014 ◽  
Vol 43 (5) ◽  
pp. 161-173
Author(s):  
Yuya HARADA ◽  
Ikuo KATAYAMA ◽  
Yoshio KONO
Keyword(s):  
Elastic Wave ◽  
Fluid Pressure ◽  
Pore Fluid ◽  
Pore Fluid Pressure ◽  
Wave Velocities

Study on the Dynamics Characteristics of Elastic Wave of Weathered Zone in Longmen Grottoes

2011 ◽  
Vol 105-107 ◽  
pp. 1509-1512
Author(s):  
Wu Xiu Ding ◽  
Hong Yi Wang
Keyword(s):  
Elastic Wave ◽  
Attenuation Coefficient ◽  
Wave Velocity ◽  
P Wave ◽  
Test Results ◽  
S Wave ◽  
Wave Velocities ◽  
Weathered Zone

Based on the test results, the wave velocity and the attenuation rule of elastic wave of weathered zone in Longmen Grottoes are studied. The wave velocity decreases with the increasing of the attenuation coefficient in a certain range. When wave velocity decreases to a certain value, there is not a relationship between wave velocity and attenuation coefficient. The attenuation coefficient thresholds of P-wave 0.01and S-wave 0.1 separate good rockmass quality from poor rockmass quality. The test results show that the elastic wave velocities of the surrounding rocks are generally high, which indicates that the rockmass skeleton is solid. But the rockmass anisotropy is obvious, which indicates that the structure planes are more developed. The results of the study are important for the protection of historical relics.

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