Effective properties of a porous medium with aligned cracks containing compressible fluid

2019 ◽  
Vol 221 (1) ◽  
pp. 60-76 ◽  
Author(s):  
Yongjia Song ◽  
Hengshan Hu ◽  
Bo Han
Keyword(s):  
Porous Medium ◽  
Wave Propagation ◽  
Elastic Scattering ◽  
Wave Velocity ◽  
Compressible Fluid ◽  
Effective Properties ◽  
P Wave ◽  
Frequency Range ◽  
P Wave Velocity ◽  
Fluid Compressibility

SUMMARY Understanding the wave propagation in fluid-saturated cracked rocks is important for detecting and characterizing cracked reservoirs and fault zones with applications in geomechanics, hydrogeology, exploration geophysics and reservoir engineering. In sedimentary rocks, microscopic-scale pores are usually filled with fluid. One logical means of modelling the essential features of such rocks is to use poroelasticity theory. But previous models of wave propagation in cracked porous medium are either restricted to low frequencies at which effects of the elastic scattering (scattering into fast-P and S waves via mode conversion at the crack faces) are negligible or to the case that the crack-filling fluid is assumed to be incompressible. To overcome these restrictions, we consider the effects of crack fluid compressibility by extending spring condition into poroelasticity and derive exact solutions of the scattering problem of an incident P wave by a circular crack containing compressible fluid in a porous medium. Based on the solutions, we develop two different effective medium models to estimate frequency-dependent effective velocity and attenuation in a fluid-saturated porous rock with a set of aligned cracks. The mixed-boundary value problem reveals that both the wave-induced fluid flow (WIFF) and elastic wave scattering can cause important velocity dispersion and attenuation. The diffusion-type WIFF dominates the velocity change and attenuation for the low frequency range, while the elastic scattering dominates them for the relatively higher frequency range. The dependences of the P-wave velocity on the crack fluid compressibility are different at different frequencies. For the WIFF-dominated frequency range and Rayleigh-scattering frequency range, the P-wave velocity decreases with the crack fluid compressibility. In contrast, for the Mie scattering frequency range, the opposite occurs (the P-wave velocity increases with the crack fluid compressibility).

scholarly journals Simulation of the effect of stress-induced anisotropy on borehole compressional wave propagation

Geophysics ◽  
2014 ◽  
Vol 79 (4) ◽  
pp. D205-D216 ◽  
Author(s):  
Xinding Fang ◽  
Michael C. Fehler ◽  
Arthur Cheng
Keyword(s):  
Wave Propagation ◽  
Stress Concentration ◽  
Elastic Properties ◽  
Wave Velocity ◽  
Wave Amplitude ◽  
P Wave ◽  
Azimuthal Variation ◽  
P Wave Velocity ◽  
Velocity Region

Formation elastic properties near a borehole may be altered from their original state due to the stress concentration around the borehole. This can lead to an incorrect estimation of formation elastic properties measured from sonic logs. Previous work has focused on estimating the elastic properties of the formation surrounding a borehole under anisotropic stress loading. We studied the effect of borehole stress concentration on sonic logging in a moderately consolidated Berea sandstone using a two-step approach. First, we used an iterative approach, which combines a rock-physics model and a finite-element method, to calculate the stress-dependent elastic properties of the rock around a borehole subjected to an anisotropic stress loading. Second, we used the anisotropic elastic model obtained from the first step and a finite-difference method to simulate the acoustic response of the borehole. Although we neglected the effects of rock failure and stress-induced crack opening, our modeling results provided important insights into the characteristics of borehole P-wave propagation when anisotropic in situ stresses are present. Our simulation results were consistent with the published laboratory measurements, which indicate that azimuthal variation of the P-wave velocity around a borehole subjected to uniaxial loading is not a simple cosine function. However, on field scale, the azimuthal variation in P-wave velocity might not be apparent at conventional logging frequencies. We found that the low-velocity region along the wellbore acts as an acoustic focusing zone that substantially enhances the P-wave amplitude, whereas the high-velocity region caused by the stress concentration near the borehole results in a significantly reduced P-wave amplitude. This results in strong azimuthal variation of P-wave amplitude, which may be used to infer the in situ stress state.

Effects of ellipsoidal heterogeneities on wave propagation in partially saturated double-porosity rocks

Geophysics ◽  
2018 ◽  
Vol 83 (3) ◽  
pp. WC71-WC81 ◽  
Author(s):  
Weitao Sun ◽  
Fansheng Xiong ◽  
Jing Ba ◽  
José M. Carcione
Keyword(s):  
Wave Propagation ◽  
Aspect Ratio ◽  
Wave Velocity ◽  
Velocity Dispersion ◽  
Laboratory Data ◽  
P Wave ◽  
Lagrange Equations ◽  
Wave Dissipation ◽  
P Wave Velocity ◽  
The Impact

Reservoir rocks are heterogeneous porous media saturated with multiphase fluids, in which strong wave dissipation and velocity dispersion are closely associated with fabric heterogeneities and patchy saturation at different scales. The irregular solid inclusions and fluid patches are ubiquitous in nature, whereas the impact of geometry on wave dissipation is still not well-understood. We have investigated the dependence of wave attenuation and velocity on patch geometry. The governing equations for wave propagation in a porous medium, containing fluid/solid heterogeneities of ellipsoidal triple-layer patches, are derived from the Lagrange equations on the basis of the potential and kinetic energies. Harmonic functions describe the wave-induced local fluid flow of an ellipsoidal patch. The effects of the aspect ratio on wave velocity are illustrated with numerical examples and comparisons with laboratory measurements. The results indicate that the P-wave velocity dispersion and attenuation depend on the aspect ratio of the ellipsoidal heterogeneities, especially in the intermediate frequency range. In the case of Fort Union sandstone, the P-wave velocity increases toward an upper bound as the aspect ratio decreases. The example of a North Sea sandstone clearly indicates that introducing ellipsoidal heterogeneities gives a better description of laboratory data than that based on spherical patches. The unexpected high-velocity values previously reported and ascribed to sample heterogeneities are explained by varying the aspect ratio of the inclusions (or patches).

Pore-scale modeling of elastic wave propagation in carbonate rocks

Geophysics ◽  
2015 ◽  
Vol 80 (1) ◽  
pp. D51-D63 ◽  
Author(s):  
Zizhen Wang ◽  
Ruihe Wang ◽  
Ralf J. Weger ◽  
Tianyang Li ◽  
Feifei Wang
Keyword(s):  
Porous Media ◽  
Wave Propagation ◽  
Elastic Wave ◽  
Pore Structure ◽  
Wave Velocity ◽  
Carbonate Rocks ◽  
P Wave ◽  
Pore Scale ◽  
Scale Modeling ◽  
P Wave Velocity

The relationship between P-wave velocity and porosity in carbonate rocks shows a high degree of variability due to the complexity of the pore structure. This variability introduces high uncertainties to seismic inversion, amplitude variation with offset analysis, porosity estimation, and pore-pressure prediction based on velocity data. Elastic wave propagation in porous media is numerically modeled on the pore scale to investigate the effects of pore structure on P-wave velocities in carbonate rocks. We built 2D models of porous media using pore structure information and the similarity principle. Then, we simulated normal incidence wave propagation using finite element analysis. Finally, the velocity was determined from received modeled signals by means of crosscorrelation. The repeatability and accuracy of this modeling process was verified carefully. Based on the modeling results, a simple formulation of Sun’s frame flexibility factor ([Formula: see text]), aspect ratio (AR, the ratio of the major axis to the minor axis), and pore density was developed. The numerical simulation results indicated that the P-wave velocity increases as a power function as the AR increases. Pores with small AR ([Formula: see text]) or large [Formula: see text] created softening effects that decrease P-wave velocity significantly. The P-wave velocity of carbonate rocks was dispersive; it depends on the ratio of the wavelength to pore size ([Formula: see text]). Such scale-dependent dispersion was more evident for carbonate rocks with higher porosity, lower AR, and/or lower P-wave impedance of pore fluids. The P-wave velocity of carbonate rocks with complicated pore geometries (low AR, high [Formula: see text], small [Formula: see text]) was much lower than that of rocks with simple pore geometries (high AR, small [Formula: see text], large [Formula: see text]) at low and high [Formula: see text]. The pore-scale modeling of elastic wave properties of porous rocks may explain the poor velocity-porosity correlation in carbonate rocks.

High-frequency seismic response during permeability reduction due to biopolymer clogging in unconsolidated porous media

Geophysics ◽  
2013 ◽  
Vol 78 (6) ◽  
pp. EN117-EN127 ◽  
Author(s):  
Tae-Hyuk Kwon ◽  
Jonathan B. Ajo-Franklin
Keyword(s):  
Porous Media ◽  
Seismic Response ◽  
Wave Velocity ◽  
Wave Attenuation ◽  
P Wave ◽  
Ultrasonic Frequency ◽  
Permeability Reduction ◽  
Frequency Range ◽  
P Wave Velocity

The accumulation of biopolymers in porous media, produced by stimulating either indigenous bacteria or artificially introduced microbes, readily blocks pore throats and can effectively reduce bulk permeability. Such a microbial clogging treatment can be used for selective plugging of permeable zones in reservoirs and is considered a potentially promising approach to enhance sweep efficiency for microbial enhanced oil recovery (MEOR). Monitoring in situ microbial growth, biopolymer formation, and permeability reduction in the reservoir is critical for successful application of this MEOR approach. We examined the feasibility of using seismic signatures (P-wave velocity and attenuation) for monitoring the in situ accumulation of insoluble biopolymers in unconsolidated sediments. Column experiments, which involved stimulating the sucrose metabolism of Leuconostoc mesenteroides and production of the biopolymer dextran, were performed while monitoring changes in permeability and seismic response using the ultrasonic pulse transmission method. We observed that L. mesenteroides produced a viscous biopolymer in sucrose-rich media. Accumulated dextran, occupying 4%–6% pore volume after [Formula: see text] days of growth, reduced permeability more than one order of magnitude. A negligible change in P-wave velocity was observed, indicating no or minimal change in compressive stiffness of the unconsolidated sediment during biopolymer formation. The amplitude of the P-wave signals decreased [Formula: see text] after [Formula: see text] days of biopolymer production; spectral ratio analysis in the 0.4–0.8-MHz band showed an approximate 30%–50% increase in P-wave attenuation ([Formula: see text]) due to biopolymer production. A flow-induced loss mechanism related to the combined grain/biopolymer structure appeared to be the most plausible mechanism for causing the observed increase in P-wave attenuation in the ultrasonic frequency range. Because permeability reduction is also closely linked to biopolymer volume, P-wave attenuation in the ultrasonic frequency range appears to be an effective indicator for monitoring in situ biopolymer accumulation and permeability reduction and could provide a useful proxy for regions with altered transport properties.

scholarly journals Geophysical and analytical determination of overstressed zones in exploited coal seam: a case study

2021 ◽  
Author(s):  
Dariusz Chlebowski ◽  
Zbigniew Burtan
Keyword(s):  
Coal Seam ◽  
Wave Velocity ◽  
Seismic Tomography ◽  
Analytical Modeling ◽  
Coal Mines ◽  
Vertical Stress ◽  
P Wave ◽  
Rockburst Hazard ◽  
State Of Stress ◽  
P Wave Velocity

AbstractA variety of geophysical methods and analytical modeling are applied to determine the rockburst hazard in Polish coal mines. In particularly unfavorable local conditions, seismic profiling, active/passive seismic tomography, as well as analytical state of stress calculating methods are recommended. They are helpful in verifying the reliability of rockburst hazard forecasts. In the article, the combined analysis of the state of stress determined by active seismic tomography and analytical modeling was conducted taking into account the relationship between the location of stress concentration zones and the level of rockburst hazard. A longwall panel in the coal seam 501 at a depth of ca.700 m in one of the hard coal mines operating in the Upper Silesian Coal Basin was a subject of the analysis. The seismic tomography was applied for the reconstruction of P-wave velocity fields. The analytical modeling was used to calculate the vertical stress states basing on classical solutions offered by rock mechanics. The variability of the P-wave velocity field and location of seismic anomaly in the coal seam in relation to the calculated vertical stress field arising in the mined coal seam served to assess of rockburst hazard. The applied methods partially proved their adequacy in practical applications, providing valuable information on the design and performance of mining operations.

Sign in / Sign up

Export Citation Format

Share Document