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.

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).

scholarly journals Effects of Pore Geometry and Pore Structure on Dry P-Wave Velocity

2016 ◽  
Vol 10 (8) ◽  
pp. 117 ◽  
Author(s):  
Suryo Prakoso ◽  
Pudji Permadi ◽  
Sonny Winardhie
Keyword(s):  
Pore Structure ◽  
Wave Velocity ◽  
P Wave ◽  
Pore Geometry ◽  
Porous Rocks ◽  
Pore System ◽  
Irregular Shapes ◽  
Factors Influencing ◽  
P Wave Velocity ◽  
Structure Similarity

The behavior of compressional or P-wave velocity passing through natural porous rocks with heterogeneous and irregular shapes of the pore system is not well understood. The present study implemented a modified Kozeny equation to characterize pore attributes, pore geometry and structure, in an attempt to investigate factors influencing the velocity. This equation is in the form of a power law one from which a concept of similarity in pore attributes can be derived. Employing a large number of data of porous sandstones, the results show that a similarity in the pore attribute plays an important role in relating the velocity with the details of geometry and structure of the pores system. For a given group of rocks having similar pore structure, an increase in the pore geometry variable, (k/f)0.5, tends to increase the velocity provided that the increase in the geometry is due to an increase in permeability followed by a decrease in porosity. Overall, the prediction of P-wave velocity is best obtained when the rocks are grouped according to pore structure similarity.

scholarly journals Optimization of Rock Physics Models by Combining the Differential Effective Medium (DEM) and Adaptive Batzle-Wang Methods in “R” Field, East Java

2019 ◽  
Vol 17 (2) ◽  
Author(s):  
M. Wahdanadi Haidar ◽  
Reza Wardhana ◽  
M. Iskan ◽  
M. Syamsu Rosid
Keyword(s):  
Elastic Modulus ◽  
Wave Velocity ◽  
Carbonate Rocks ◽  
Effective Medium ◽  
Carbonate Reservoir ◽  
P Wave ◽  
S Wave ◽  
P Wave Velocity ◽  
Reservoir Conditions ◽  
Pore Types

The pore systems in carbonate reservoirs are more complex than the pore systems in clastic rocks. There are three types of pores in carbonate rocks: interparticle pores, stiff pores and cracks. The complexity of the pore types can lead to changes in the P-wave velocity by up to 40%, and carbonate reservoir characterization becomes difficult when the S-wave velocity is estimated using the dominant interparticle pore type only. In addition, the geometry of the pores affects the permeability of the reservoir. Therefore, when modelling the elastic modulus of the rock it is important to take into account the complexity of the pore types in carbonate rocks. The Differential Effective Medium (DEM) is a method for modelling the elastic modulus of the rock that takes into account the heterogeneity in the types of pores in carbonate rocks by adding pore-type inclusions little by little into the host material until the required proportion of the material is reached. In addition, the model is optimized by calculating the bulk modulus of the fluid filler porous rock under reservoir conditions using the Adaptive Batzle-Wang method. Once a fluid model has been constructed under reservoir conditions, the model is entered as input for the P-wave velocity model, which is then used to estimate the velocity of the S-wave and the proportion of primary and secondary pore types in the rock. Changes in the characteristics of the P-wave which are sensitive to the presence of fluid lead to improvements in the accuracy of the P-wave model, so the estimated S-wave velocity and the calculated ratio of primary and secondary pores in the reservoir are more reliable.

Pore-pressure prediction in carbonate rock using wavelet transformation

Geophysics ◽  
2014 ◽  
Vol 79 (4) ◽  
pp. D243-D252 ◽  
Author(s):  
Fu Yu ◽  
Yan Jin ◽  
Kang Ping Chen ◽  
Mian Chen
Keyword(s):  
Pore Pressure ◽  
Wave Velocity ◽  
Carbonate Rocks ◽  
Wavelet Transformation ◽  
Pressure Change ◽  
P Wave ◽  
Small Scale ◽  
Prediction Methods ◽  
P Wave Velocity ◽  
Pore Pressure Prediction

Accurate prediction of pore pressure can assist engineers to better work out and optimize an oilfield development plan. Because the P-wave velocity only experiences small-scale fluctuations for pore-pressure change in carbonate rocks, existing well-known pore-pressure prediction methods are incapable of predicting pore pressure in carbonate rocks with field-required accuracy. We evaluated a new method based on the P-wave velocity decomposition and wavelet transformation to predict pore pressure in carbonate rocks. The P-wave velocity was decomposed into contributions from the pore fluid and the rock framework using Biot’s theory. The effect of lithology, pore structure, porosity, and pore pressure on P-wave velocity was studied by theoretical analysis and experiments. Rapid triaxial rock-system tests were carried out to measure the P- and S-wave velocities when pore pressure, pore structure, and porosity were changed, and X-ray diffraction tests were used to measure mineral components. The small-scale fluctuations of the P-wave velocity can be extracted and amplified using wavelet transformation. We found that the small-scale fluctuations of the P-wave velocity were caused by pore-pressure change in carbonate rocks and the large-scale fluctuations of the P-wave velocity depended on the rock framework. Overpressure formation can be identified by the high-frequency detail of wavelet transformation of P-wave velocity. A pore-pressure prediction model relating the contribution from the pore fluid to the P-wave velocity was developed. This model is an improvement over existing pore-pressure prediction methods that mainly rely on empirical relations between the P-wave velocity and the pore pressure. This new method was successfully applied to carbonate rocks in Tazhong Block, Tarim oilfield, demonstrating the feasibility of the proposed pore-pressure prediction method.

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).

Permeability dependence of porosity and p-wave velocity in carbonate rocks

2016 ◽  
Author(s):  
Grazielle Oliveira ◽  
Marco Ceia ◽  
Roseane Missagia ◽  
Victor Santos ◽  
Irineu Lima Neto
Keyword(s):  
Wave Velocity ◽  
Carbonate Rocks ◽  
P Wave ◽  
P Wave Velocity
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