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1.
Stiffness variations in carbonates may be described as resulting from different concentrations of flat compliant pores or cracks, which can have a significant effect on the effective stiffness and acoustic properties (e.g., velocities and attenuations) of dry as well as saturated carbonates, although they carry extremely little porosity. As shown in this paper, the effects of dual porosity and wave-induced fluid flow or pore pressure communication may also play a significant role. On the basis of a previously published T-matrix approach to model the effective viscoelastic properties of cracked porous media, we illustrate the (frequency-dependent) effects of wave-induced fluid flow (mainly squirt flow) or pore pressure communication for a model structure consisting of a mixture of fluid-saturated porous grains and fluid-saturated cavities (vugs, etc.) that are embedded in a solid matrix associated with carbonates. We assume that the pores within the porous grains are decoupled from the pores in the solid matrix (and possibly saturated with different fluids) but that each pore system at the micro and/or mesoscale may or may not be connected. For each of four different connectivity models, we present numerical results for four different cases of microstructure (that emphasize the importance of cracks and flat compliant pores). Our numerical results indicate that the velocity and attenuation spectra of carbonates vary significantly, even when the crack density and all other volume concentrations are constant. 相似文献
2.
Analytical approximations of bulk and shear moduli for dry rock based on the differential effective medium theory 总被引：2，自引：0，他引：2
Differential effective medium theory has been applied to determine the elastic properties of porous media. The ordinary differential equations for bulk and shear moduli are coupled and it is more difficult to obtain accurate analytical formulae about the moduli of dry porous rock. In this paper, in order to decouple these equations we first substitute an analytical approximation for the dry‐rock modulus ratio into the differential equation and derive analytical solutions of the bulk and shear moduli for dry rock with three specific pore shapes: spherical pores, needle‐shaped pores and penny‐shaped cracks. Then, the validity of the analytical approximations is tested by integrating the full differential effective medium equation numerically. The analytical formulae give good estimates of the numerical results over the whole porosity range for the cases of the three given pore shapes. These analytical formulae can be further simplified under the assumption of small porosity. The simplified formulae for spherical pores are the same as Mackenzie's equations. The analytical formulae are relatively easy to analyse the relationship between the elastic moduli and porosity or pore shapes and can be used to invert some rock parameters such as porosity or pore aspect ratio. The predictions of the analytical formulae for experimental data show that the formulae for penny‐shaped cracks are suitable to estimate the elastic properties of micro‐crack rock such as granite, they can be used to estimate the crack aspect ratio while the crack porosity is known and also to estimate the crack porosity evolution with pressure if the crack aspect ratio is given. 相似文献
3.
Differential effective medium (DEM) theory is applied to determine the elastic properties of dry rock with spheroidal pores. These pores are assumed to be randomly oriented. The ordinary differential equations for bulk and shear moduli are coupled and it is more difficult to obtain accurate analytical formulae about the moduli of dry porous rock. In this paper, we derive analytical solutions of the bulk and shear moduli for dry rock from the differential equations by applying an analytical approximation for dry-rock modulus ratio, in order to decouple these equations. Then, the validity of this analytical approximation is tested by integrating the full DEM equation numerically. The analytical formulae give good estimates of the numerical results over the whole porosity range. These analytical formulae can be further simplified under the assumption of small porosity. The simplified formulae for spherical pores (i.e., the pore aspect ratio is equal to 1) are the same as Mackenzie's equations. The analytical formulae are relatively easy to analyze the relationship between the elastic moduli and porosity or pore shapes, and can be used to invert some rock parameters such as porosity or pore aspect ratio. The predictions of the analytical formula for the sandstone experimental data show that the analytical formulae can accurately predict the variations of elastic moduli with porosity for dry sandstones. The effective elastic moduli of these sandstones can be reasonably well characterized by spheroidal pores, whose pore aspect ratio was determined by minimizing the error between theoretical predictions and experimental measurements. For sandstones the pore aspect ratio increases as porosity increases if the porosity is less than 0.15, whereas the pore aspect ratio remains relatively stable (about 0.14) if the porosity is more than 0.15. 相似文献
4.
Yongyang Sun Boris Gurevich Maxim Lebedev Stanislav Glubokovskikh Vassili Mikhaltsevitch Junxin Guo 《Geophysical Prospecting》2019,67(4):888-899
Quantifying the effects of pore-filling materials on elastic properties of porous rocks is of considerable interest in geophysical practice. For rocks saturated with fluids, the Gassmann equation is proved effective in estimating the exact change in seismic velocity or rock moduli upon the changes in properties of pore infill. For solid substance or viscoelastic materials, however, the Gassmann theory is not applicable as the rigidity of the pore fill (either elastic or viscoelastic) prevents pressure communication in the pore space, which is a key assumption of the Gassmann equation. In this paper, we explored the elastic properties of a sandstone sample saturated with fluid and solid substance under different confining pressures. This sandstone sample is saturated with octadecane, which is a hydrocarbon with a melting point of 28°C, making it convenient to use in the lab in both solid and fluid forms. Ultrasonically measured velocities of the dry rock exhibit strong pressure dependency, which is largely reduced for the filling of solid octadecane. Predictions by the Gassmann theory for the elastic moduli of the sandstone saturated with liquid octadecane are consistent with ultrasonic measurements, but underestimate the elastic moduli of the sandstone saturated with solid octadecane. Our analysis shows that the difference between the elastic moduli of the dry and solid-octadecane-saturated sandstone is controlled by the squirt flow between stiff, compliant, and the so-called intermediate pores (with an aspect ratio larger than that of compliant pore but much less than that of stiff pores). Therefore, we developed a triple porosity model to quantify the combined squirt flow effects of compliant and intermediate pores saturated with solid or viscoelastic infill. Full saturation of remaining stiff pores with solid or viscoelastic materials is then considered by the lower embedded bound theory. The proposed model gave a reasonable fit to the ultrasonic measurements of the elastic moduli of the sandstone saturated with liquid or solid octadecane. Comparison of the predictions by the new model to other solid substitution schemes implied that accounting for the combined effects of compliant and intermediate pores is necessary to explain the solid squirt effects. 相似文献
5.
经典的微分等效介质(DEM)理论可用于确定多孔介质的弹性性质,但由于缺乏多重孔DEM方程,其估计的多重孔岩石的等效弹性模量依赖于包裹体(即不同孔隙纵横比的孔或缝)的添加顺序.本文首先从Kuster-Toksöz理论出发建立了Zimmermann和Norris两种形式的多重孔DEM方程.Norris形式的多重孔DEM方程预测的等效弹性模量总是位于Hashin-Shtrikman上下限内,而Zimmermann形式的多重孔DEM方程有时会越界.然后,通过使用干燥岩石模量比的解析近似式,对两个相互耦合的Norris形式DEM方程进行解耦得到干燥多重孔岩石的体积和剪切模量解析式.用全DEM方程的数值解对解析近似式的有效性进行了测试,解析公式的计算结果在整个孔隙度分布区间与数值解吻合良好.对实验室测量数据在假设岩石含有双重孔隙的情形下用双重孔DEM解析公式对岩石的弹性模量进行了预测,结果表明,解析式准确地预测了弹性模量随孔隙度的变化.双重孔(即软、硬孔)DEM解析模型可用来反演各孔隙类型的孔隙体积比,它可以通过实验室测量与理论预测之间的平方误差最小反演得到.砂岩样品的反演结果揭示,软孔的孔隙体积百分比与粘土含量没有明显的相关性. 相似文献
6.
Experimental verification of effective anisotropic crack theories in variable crack aspect ratio medium 
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下载免费PDF全文 Jessica P. Henriques Jose J. S. de Figueiredo Leo K. Santos Daniel L. Macedo Icaro Coutinho Carolina B. da Silva Alberto L. Melo Mykel Sousa Felipe L. Azevedo 《Geophysical Prospecting》2018,66(1):141-156
Physical modelling of cracked/fractured media using downscaled laboratory experiments has been used with great success as a useful alternative for understanding the effect of anisotropy in the hydrocarbon reservoir characterization and in the crustal and mantle seismology. The main goal of this work was to experimentally verify the predictions of effective elastic parameters in anisotropic cracked media by Hudson and Eshelby–Cheng's effective medium models. For this purpose, we carried out ultrasonic measurements on synthetic anisotropic samples with low crack densities and different aspect ratios. Twelve samples were prepared with two different crack densities, 5% and 8%. Three samples for each crack density presented cracks with only one crack aspect ratio, whereas other three samples for each crack density presented cracks with three different aspect ratios in their composition. It results in samples with aspect ratio values varying from 0.13 to 0.26. All the cracked samples were simulated by penny‐shaped rubber inclusions in a homogeneous isotropic matrix made with epoxy resin. Moreover, an isotropic sample for reference was constructed with epoxy resin only. Regarding velocity predictions performed by the theoretical models, Eshelby–Cheng shows a better fit when compared with the experimental results for samples with single and mix crack aspect ratio (for both crack densities). From velocity values, our comparisons were also performed in terms of the ε, γ, and δ parameters (Thomsen parameters). The results show that Eshelby–Cheng effective medium model fits better with the measurements of ε and γ parameters for crack samples with only one type of crack aspect ratio. 相似文献
7.
Yu-Qian Guo Hong-Da Ma Kai-Bo Shi Hong Cao Lu-Zhong Huang Feng-Chang Yao Tian-Yue Hu 《应用地球物理》2013,10(4):411-422
Most of the carbonates in the Tarim Basin in northwest China are low-porosity and low-permeability rocks. Owing to the complexity of porosity in carbonates, conventional rockphysics models do not describe the relation between velocity and porosity for the Tarim Basin carbonates well. We propose the porous-grain-upper-boundary (PGU) model for estimating the relation between velocity and porosity for low-porosity carbonates. In this model, the carbonate sediments are treated as packed media of porous elastic grains, and the carbonate pores are divided into isolated and connected pores The PGU model is modified from the porous-grain-stiff-sand (PGST) model by replacing the critical porosity with the more practical isolated porosity. In the implementation, the effective elastic constants of the porous grains are calculated by using the differential effective medium (DEM) model. Then, the elastic constants of connected porous grains in dry rocks are calculated by using the modified upper Hashin-Shtrikman bound. The application to the Tarim carbonates shows that relative to other conventional effective medium models the PGU model matches the well log data well. 相似文献
8.
9.
An approach to determining the effective elastic moduli of rocks with double porosity is presented. The double‐porosity medium is considered to be a heterogeneous material composed of a homogeneous matrix with primary pores and inclusions that represent secondary pores. Fluid flows in the primary‐pore system and between primary and secondary pores are neglected because of the low permeability of the primary porosity. The prediction of the effective elastic moduli consists of two steps. Firstly, we calculate the effective elastic properties of the matrix with the primary small‐scale pores (matrix homogenization). The porous matrix is then treated as a homogeneous isotropic host in which the large‐scale secondary pores are embedded. To calculate the effective elastic moduli at each step, we use the differential effective medium (DEM) approach. The constituents of this composite medium – primary pores and secondary pores – are approximated by ellipsoidal or spheroidal inclusions with corresponding aspect ratios. We have applied this technique in order to compute the effective elastic properties for a model with randomly orientated inclusions (an isotropic medium) and aligned inclusions (a transversely isotropic medium). Using the special tensor basis, the solution of the one‐particle problem with transversely isotropic host was obtained in explicit form. The direct application of the DEM method for fluid‐saturated pores does not account for fluid displacement in pore systems, and corresponds to a model with isolated pores or the high‐frequency range of acoustic waves. For the interconnected secondary pores, we have calculated the elastic moduli for the dry inclusions and then applied Gassmann's tensor relationships. The simulation of the effective elastic characteristic demonstrated that the fluid flow between the connected secondary pores has a significant influence only in porous rocks containing cracks (flattened ellipsoids). For pore shapes that are close to spherical, the relative difference between the elastic velocities determined by the DEM method and by the DEM method with Gassmann's corrections does not exceed 2%. Examples of the calculation of elastic moduli for water‐saturated dolomite with both isolated and interconnected secondary pores are presented. The simulations were verified by comparison with published experimental data. 相似文献
10.
The subject of this paper is the treatment of rocks - and, especially, fluid-saturated and partially saturated reservoir rocks, as composite visco-elastic media. By this we mean to study and partially answer the question of how the effective material (frequency-dependent and complex-valued stiffness/density) parameters can be estimated from a knowledge of the constituents of the rocks, their volume fractions, the statistical distribution of sizes, shapes, orientations and positions of the individual particles (minerals of quartz, clay, etc.) and cavities (pores, cracks, etc.); in addition to parameters related to the fluid and its ability to flow, at the scale of the microstructure as well as that of the wavelength (assumed to be long compared to the scale-size of the microstructure).Our approach is to develop and combine a theory of stochastic waves with established results for the micromechanics of defects in solids, as well as state-of-the-art models of wave-induced fluid flow. Specifically, we first derive an exact formal expression for the effective material parameters in terms of a dynamic T-matrix for the material, which satisfies a single integral equation of the Lippmann-Schwinger type (known from quantum scattering theory), but formulated in an abstract vector space, associated with the combination of the strain and velocity fields into a more general state vector . Inclusions-based models are developed on the basis of standard many-body techniques, known from the static T-matrix approach as well as nuclear collision theory. The t-matrix of a low-aspect-ratio spheroidal crack is expressed in terms of the familiar displacement discontinuity parameters of Hudson, via the so-called K-tensor, which is of interest in itself, for example, when connecting cracks to pores (in the presence of multiple solid constituents) on the basis of an expression for the t-matrix of a communicating cavity.The present theory can in principle be used beyond the Rayleigh limit, but explicit estimates of the effective material parameters have so far been derived only under the assumption that (scattering attenuation can be ignored) the wavelength is large compared to the scale-size of a representative volume element. Starting with the dynamic equations of motion, we show that the behaviour of the mean wave in the Rayleigh limit is indeed determined by the effective stiffness tensor associated with a static theory of composites, in conjunction with the spatially averaged density for the heterogeneous material as a whole. Thus, we have provided justification to the procedure we used in a series of related papers, where we started out with the static equilibrium condition and employed the elastic/visco-elastic correspondence principle. Numerical examples (dealing with the effects of randomly oriented cracks on the isotropic velocity and attenuation spectra of a dual porosity model of clay-sand mixtures, and the effects of spatial distribution on the anisotropic attenuation spectra of fully aligned cracks that are partially saturated with two different fluids) will be provided in order to complement those in our earlier papers. 相似文献
11.
Morten Jakobsen 《Studia Geophysica et Geodaetica》2012,56(1):1-20
Forward seismic modelling in the acoustic approximation, for variable velocity but constant density, is dealt with. The wave
equation and the boundary conditions are represented by a volume integral equation of the Lippmann-Schwinger (LS) or Fredholm
type. A T-matrix (or transition operator) approach from quantum mechanical potential scattering theory is used to derive a
family of linear and nonlinear approximations (cluster expansions), as well as an exact numerical solution of the LS equation.
For models of 4D anomalies involving small or moderate contrasts, the Born approximation gives identical numerical results
as the first-order t-matrix approximation, but the predictions of an exact T-matrix solution can be quite different (depending
on spatial extention of the perturbations). For models of fluid-saturated cavities involving large or huge contrasts, the
first-order t-matrix approximation is much more accurate than the Born approximation, although it does not lead to significantly
more time-consuming computations. If the spatial extention of the perturbations is not too large, it is practical to use the
exact T-matrix solution which allows for arbitrary contrasts and includes all the effects of multiple scattering. 相似文献
12.
Effect of micro‐inhomogeneity on the effective stress coefficients and undrained bulk modulus of a poroelastic medium: a double spherical shell model 下载免费PDF全文
下载免费PDF全文 Although most rocks are complex multi‐mineralic aggregates, quantitative interpretation workflows usually ignore this complexity and employ Gassmann equation and effective stress laws that assume a micro‐homogeneous (mono‐mineralic) rock. Even though the Gassmann theory and effective stress concepts have been generalized to micro‐inhomogeneous rocks, they are seldom if at all used in practice because they require a greater number of parameters, which are difficult to measure or infer from data. Furthermore, the magnitude of the effect of micro‐heterogeneity on fluid substitution and on effective stress coefficients is poorly understood. In particular, it is an open question whether deviations of the experimentally measurements of the effective stress coefficients for drained and undrained elastic moduli from theoretical predictions can be explained by the effect of micro‐heterogeneity. In an attempt to bridge this gap, we consider an idealized model of a micro‐inhomogeneous medium: a Hashin assemblage of double spherical shells. Each shell consists of a spherical pore surrounded by two concentric spherical layers of two different isotropic minerals. By analyzing the exact solution of this problem, we show that the results are exactly consistent with the equations of Brown and Korringa (which represent an extension of Gassmann's equation to micro‐inhomogeneous media). We also show that the effective stress coefficients for bulk volume α, for porosity n? and for drained and undrained moduli are quite sensitive to the degree of heterogeneity (contrast between the moduli of the two mineral components). For instance, while for micro‐homogeneous rocks the theory gives n? = 1, for strongly micro‐inhomogenous rocks, n? may span a range of values from –∞ to ∞ (depending on the contrast between moduli of inner and outer shells). Furthermore, the effective stress coefficient for pore volume (Biot–Willis coefficient) α can be smaller than the porosity ?. Further studies are required to understand the applicability of the results to realistic rock geometries. 相似文献
13.
地质成因和构造/热应力导致地壳岩石中的孔隙结构（裂隙和粒间孔）的变化.影响岩石黏弹性的因素包括压力、孔隙度、孔隙中包含的流体和孔隙几何形状等.相对于岩石中的硬孔隙,岩石黏弹性（衰减和频散）受软孔隙（裂隙）的影响更大.本文选取三块白云岩样本,进行了不同围压和流体条件下的超声波实验测量.利用CPEM（Cracks and Pores Effective Medium,裂隙和孔隙有效介质）模型获得了岩石高、低频极限的弹性模量,并通过Zener体（标准线性体）模型将CPEM模型拓展到全频带而得到CPEM-Zener模型,用该模型拟合岩石松弛和非松弛状态下的实验数据,本文得到平均裂隙纵横比和裂隙孔隙度以及纵波速度和品质因子随频率的变化关系.结果表明,饱水岩石的平均裂隙纵横比和裂隙孔隙度均高于饱油岩石,随着压差（围压和孔隙压力的差值）的增加,饱油岩石中的裂隙首先闭合.并且压差在70 MPa以内时,随着压差增大,岩石的平均裂隙纵横比和裂隙孔隙度在饱水和饱油时的差值增大,此时流体类型对于岩石裂隙的影响越来越显著,此外,对饱水岩石,平均裂隙纵横比随压差增加而增大,这可能是由于岩石中纵横比较小的裂隙会随压差增大而逐渐趋于闭合.在饱水和饱油岩石中,裂隙孔隙度和裂隙密度都随着压差增加而减小.通过对裂隙密度和压差的关系进行指数拟合,本文获得压差趋于0时的裂隙密度,且裂隙密度随孔隙度增大而增大,增大速率随压差增加而降低.针对饱水和饱油的白云岩样本,CPEM-Zener模型预测的纵波频散随压差增大而减小,此变化趋势和实验测得的逆品质因子随压差的变化关系基本一致,由此进一步验证了模型的实用性.本研究对岩石的孔隙结构和黏弹性分析以及声波测井、地震勘探的现场应用有指导意义. 相似文献
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15.
This paper is concerned with numerical tests of several rock physical relationships. The focus is on effective velocities and scattering attenuation in 3D fractured media. We apply the so‐called rotated staggered finite‐difference grid (RSG) technique for numerical experiments. Using this modified grid, it is possible to simulate the propagation of elastic waves in a 3D medium containing cracks, pores or free surfaces without applying explicit boundary conditions and without averaging the elastic moduli. We simulate the propagation of plane waves through a set of randomly cracked 3D media. In these numerical experiments we vary the number and the distribution of cracks. The synthetic results are compared with several (most popular) theories predicting the effective elastic properties of fractured materials. We find that, for randomly distributed and randomly orientated non‐intersecting thin penny‐shaped dry cracks, the numerical simulations of P‐ and S‐wave velocities are in good agreement with the predictions of the self‐consistent approximation. We observe similar results for fluid‐filled cracks. The standard Gassmann equation cannot be applied to our 3D fractured media, although we have very low porosity in our models. This is explained by the absence of a connected porosity. There is only a slight difference in effective velocities between the cases of intersecting and non‐intersecting cracks. This can be clearly demonstrated up to a crack density that is close to the connectivity percolation threshold. For crack densities beyond this threshold, we observe that the differential effective‐medium (DEM) theory gives the best fit with numerical results for intersecting cracks. Additionally, it is shown that the scattering attenuation coefficient (of the mean field) predicted by the classical Hudson approach is in excellent agreement with our numerical results. 相似文献
16.
The modelling of elastic waves in fractured media with an explicit finite‐difference scheme causes instability problems on a staggered grid when the medium possesses high‐contrast discontinuities (strong heterogeneities). For the present study we apply the rotated staggered grid. Using this modified grid it is possible to simulate the propagation of elastic waves in a 2D or 3D medium containing cracks, pores or free surfaces without hard‐coded boundary conditions. Therefore it allows an efficient and precise numerical study of effective velocities in fractured structures. We model the propagation of plane waves through a set of different, randomly cracked media. In these numerical experiments we vary the wavelength of the plane waves, the crack porosity and the crack density. The synthetic results are compared with several static theories that predict the effective P‐ and S‐wave velocities in fractured materials in the long wavelength limit. For randomly distributed and randomly orientated, rectilinear, non‐intersecting, thin, dry cracks, the numerical simulations of velocities of P‐, SV‐ and SH‐waves are in excellent agreement with the results of the modified (or differential) self‐consistent theory. On the other hand for intersecting cracks, the critical crack‐density (porosity) concept must be taken into account. To describe the wave velocities in media with intersecting cracks, we propose introducing the critical crack‐density concept into the modified self‐consistent theory. Numerical simulations show that this new formulation predicts effective elastic properties accurately for such a case. 相似文献
17.
Wyllie's time-average equation and subsequent refinements have been used for over 20 years to estimate the porosity of reservoir rocks from compressional (P)-wave velocity (or its reciprocal, transit time) recorded on a sonic log. This model, while simple, needs to be more convincingly explained in theory and improved in practice, particularly by making use of shear (S)-wave velocity. One of the most important, although often ignored, factors affecting elastic velocities in a rock is pore structure, which is also a controlling factor for transport properties of a rock. Now that S-wave information can be obtained from the sonic log, it may be used with P-waves to provide a better understanding of pore structure. A new acoustic velocities-to-porosity transform based on an elastic velocity model developed by Kuster and Toksöz is proposed. Employing an approximation to an equivalent pore aspect ratio spectrum, pore structure for reservoir rocks is taken into account, in addition to total pore volume. Equidimensional pores are approximated by spheres and rounded spheroids, while grain boundary pores and flat pores are approximated by low aspect ratio cracks. An equivalent pore aspect ratio spectrum is characterized by a power function which is determined by compressional-and shear-wave velocities, as well as by matrix and inclusion properties. As a result of this more sophisticated elastic model of porous rocks and a stricter theory of elastic wave propagation, the new method leads to a more satisfactory interpretation and fuller use of seismic and sonic log data. Calculations using the new transform on data for sedimentary rocks, obtained from published literature and laboratory measurements, are presented and compared at atmospheric pressure with those estimated from the time-average equation. Results demonstrate that, to compensate for additional complexity, the new method provides more detailed information on pore volume and pore structure of reservoir rocks. Examples are presented using a realistic self-consistent averaging scheme to consider interactions between pores, and the possibility of extending the method to complex lithologies and shaly rocks is discussed. 相似文献
18.
R. Agersborg M. Jakobsen B. O. Ruud T. A. Johansen 《Studia Geophysica et Geodaetica》2007,51(1):89-118
An effective medium model for the stress-dependent seismic properties of fractured reservoirs is developed here on the basis
of a combination of a general theory of viscoelastic waves in rock-like composites with recently published formulae for deformation
of communicating and interacting cavities (interconnected pores/cracks and fractures at finite concentration) under drained
loading. The inclusion-based model operates with spheroidal cavities at two different length scales; namely, the microscopic
scale of the pores and (grain-boundary) cracks, and the mesoscopic scale of the fractures (controlling the flow of fluid).
The different cavity types can in principle have any orientation and aspect ratio, but the microscopic pores/cracks and mesoscopic
fractures were here assumed to be randomly and vertically oriented, respectively. By using three different aspect ratios for
the relatively round pores (representing the stiff part of the pore space) and a distribution of aspect ratios for the relatively
flat cracks (representing the compliant part of the pore space), we obtained a good fit between theoretical predictions and
ultrasonic laboratory measurements on an unfractured rock sample under dry conditions. By using a single aspect ratio for
the mesoscopic fractures, we arrived at a higher-order microstructural model of fractured porous media which represents a
generalization of the first-order model developed by Chapman et al. (2002,2003). The effect of cavity size was here modelled
under the assumption that the characteristic time for wave-induced (squirt) flow at the scale of a particular cavity (pore/crack
vs. fracture) is proportional with the relevant scale-size. In the modelling, we investigate the effect of a decreasing pore
pressure with constant confining pressure (fixed depth), and hence, increasing effective pressure. The analysis shows that
the attenuation-peak due to the mesoscopic fractures in the reservoir will move downward in frequency as the effective pressure
increases. In the range of seismic frequencies, our modelling indicates that the P-wave velocities may change by more than
20% perpendicular to the fractures and close to 10% parallel to the fractures. In comparison, the vertical S-wave velocities
change by only about 5% for both polarization directions (perpendicular and parallel to the fractures) when the effective
pressure increases from 0 to 15 MPa. This change is mainly due to the overall change in porosity with pressure. The weak pressure
dependence is a consequence of the fact that the S waves will only sense if the fractures are open or not, and since all the
fractures have the same aspect ratio, they will close at the same effective pressure (which is outside the analysed interval).
Approximate reflection coefficients were computed for a model consisting of the fractured reservoir embedded as a layer in
an isotropic shale and analysed with respect to variations in Amplitude Versus Offset and aZimuth (AVOZ) properties at seismic
frequencies for increasing effective pressure. For the P-P reflections at the top of the reservoir, it is found that there
is a significant dependence on effective pressure, but that the variations with azimuth and offset are small. The lack of
azimuthal dependence may be explained from the approximate reflection coefficient formula as a result of cancellation of terms
related to the S-wave velocity and the Thomson’s anisotropy parameter δ. For the P-S reflection, the azimuthal dependence
is larger, but the pressure dependence is weaker (due to a single aspect ratio for the fractures).
Finally, using the effective stiffness tensor for the fractured reservoir model with a visco-elastic finite-difference code,
synthetic seismograms and hodograms were computed. From the seismograms, attenuation changes in the P wave reflected at the
bottom of the reservoir can be observed as the effective pressure increases. S waves are not much affected by the fractures
with respect to attenuation, but azimuthal dependence is stronger than for P waves, and S-wave splitting in the bottom reservoir
P-S reflection is clearly seen both in the seismograms and hodograms. From the hodograms, some variation in the P-S reflection
with effective pressure can also be observed. 相似文献
19.
分布于地震破裂带上的断层岩具有高孔隙度的特征.该特点造成了其弹性波速度与结晶岩石和沉积岩存在明显的差异.确定断层岩的弹性波速度与孔隙度和矿物组成的关系对于利用地震资料探测深部断层和测井资料的解释至关重要.在10~600 MPa条件下,本文对地震断层岩的纵波波速（Vp）和总孔隙度（φt）进行了测量,并深入分析了Vp与孔隙度的关系.结果表明在10~600 MPa的压力范围内,Vp（p）随着压力的增高呈现对数增加,其增长率随着压力的上升而逐渐减小,遵从∂Vp（p）/∂p=av/p的变化规律.断层岩中的孔隙度随着压力的增高呈对数减小.与传统的认识不同,实验发现在压力高达600 MPa以上,大多数断层岩中仍然可以残留可观的孔隙量.分析显示Vp与总孔隙度及总粘土含量呈负线性相关.该发现有助于认识深部流体的活动通道特征,有助于理解断层带中存在大量粘土矿物、断层带内的物质可被大量带出、围陷波的形成等地质和地球物理现象. 相似文献
20.
A computational procedure for two-dimensional finite-element analysis of dam–water–sediment–rock systems subjected to seismic excitations is reviewed. In particular, the semidiscrete approximation of the water–sediment–rock region on the upstream side of the dam by means of a hyperelement is described in detail. The sediment is represented in the hyperelement as a fluid-filled porous solid on the basis of the Biot theory of wave propagation in poroelastic media while the water is taken as a compressible, inviscid fluid and the rock as a viscoelastic solid. An application of the procedure to a study of the effects of sediment porosity and thickness on the response of a model dam to horizontal and vertical ground motions is presented and discussed. 相似文献