共查询到20条相似文献，搜索用时 15 毫秒
1.
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
2.
We design a velocity–porosity model for sand-shale environments with the emphasis on its application to petrophysical interpretation of compressional and shear velocities. In order to achieve this objective, we extend the velocity–porosity model proposed by Krief et al., to account for the effect of clay content in sandstones, using the published laboratory experiments on rocks and well log data in a wide range of porosities and clay contents. The model of Krief et al. works well for clean compacted rocks. It assumes that compressional and shear velocities in a porous fluid-saturated rock obey Gassmann formulae with the Biot compliance coefficient. In order to use this model for clay-rich rocks, we assume that the bulk and shear moduli of the grain material, and the dependence of the compliance on porosity, are functions of the clay content. Statistical analysis of published laboratory data shows that the moduli of the matrix grain material are best defined by low Hashin–Shtrikman bounds. The parameters of the model include the bulk and shear moduli of the sand and clay mineral components as well as coefficients which define the dependence of the bulk and shear compliance on porosity and clay content. The constants of the model are determined by a multivariate non-linear regression fit for P- and S-velocities as functions of porosity and clay content using the data acquired in the area of interest. In order to demonstrate the potential application of the proposed model to petrophysical interpretation, we design an inversion procedure, which allows us to estimate porosity, saturation and/or clay content from compressional and shear velocities. Testing of the model on laboratory data and a set of well logs from Carnarvon Basin, Australia, shows good agreement between predictions and measurements. This simple velocity-porosity-clay semi-empirical model could be used for more reliable petrophysical interpretation of compressional and shear velocities obtained from well logs or surface seismic data. 相似文献
3.
Although Gassmann fluid substitution is standard practice for time-lapse studies, its validity in the field environment rests upon a number of underlying assumptions. The impact of violation on the predictions of Gassmann equations can only ultimately be validated by in situ testing in real geological environments. In this paper we show a workflow that we developed to test Gassmann fluid substitution by comparing saturated P-wave moduli computed from dry core measurements against those obtained from sonic and density logs. The workflow has been tested on 43 samples taken from a 45 m turbidite reservoir from the Campos Basin, offshore Brazil. The results show good statistical agreement between the P-wave elastic moduli computed from cores using the Gassmann equation with the corresponding moduli computed from log data. This confirms that all the assumptions of the Gassmann are adequate within the measurement error and natural variability of elastic properties. These results provide further justification for using the Gassmann theory to interpret time-lapse effects in this sandstone reservoir and in similar geological formations. 相似文献
4.
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
5.
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
6.
A critical porosity model establishes the empirical relationship between a grain matrix and a dry rock by the concept of critical porosity. The model is simple and practical and widely used. But the critical porosity in the model is a fixed value that cannot relate to pore structure. The aim of this paper is to establish the theoretical relationship between critical porosity and pore structure by combining Kuster–Toksöz theory with the critical porosity model. Different from the traditional critical porosity model, critical porosity is not an empirical value but varied with pore shape and the ratio of bulk modulus versus shear modulus of the grain matrix. The substitution of the theoretical relationship into Kuster–Toksöz theory will generate the formulae for the bulk and shear moduli of multiple-porosity dry rocks, which is named the multiple-porosity variable critical porosity model. The new model has been used to predict elastic moduli for sandstone and carbonate rock. We compare the modelling results for P- and S-wave velocities and elastic moduli with the experimental data. The comparison shows that the new model can be used to describe the elastic properties for the rocks with multiple pore types. 相似文献
7.
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
8.
We obtain the wave velocities of clay-bearing sandstones as a function of clay content, porosity and frequency. Unlike previous theories, based simply on slowness and/or moduli averaging or two-phase models, we use a Biot-type three-phase theory that considers the existence of two solids (sand grains and clay particles) and a fluid. The theory, which is consistent with the critical porosity concept, uses three free parameters that determine the dependence of the dry-rock moduli of the sand and clay matrices as a function of porosity and clay content.
Testing of the model with laboratory data shows good agreement between predictions and measurements. In addition to a rock physics model that can be useful for petrophysical interpretation of wave velocities obtained from well logs and surface seismic data, the model provides the differential equation for computing synthetic seismograms in inhomogeneous media, from the seismic to the ultrasonic frequency bands. 相似文献
Testing of the model with laboratory data shows good agreement between predictions and measurements. In addition to a rock physics model that can be useful for petrophysical interpretation of wave velocities obtained from well logs and surface seismic data, the model provides the differential equation for computing synthetic seismograms in inhomogeneous media, from the seismic to the ultrasonic frequency bands. 相似文献
9.
Fracture detection and fluid identification are important tasks for a fractured reservoir characterization. Our goal is to demonstrate a direct approach to utilize azimuthal seismic data to estimate fluid bulk modulus, porosity, and dry fracture weaknesses, which decreases the uncertainty of fluid identification. Combining Gassmann’s (Vier. der Natur. Gesellschaft Zürich 96:1–23, 1951) equations and linear-slip model, we first establish new simplified expressions of stiffness parameters for a gas-bearing saturated fractured rock with low porosity and small fracture density, and then we derive a novel PP-wave reflection coefficient in terms of dry background rock properties (P-wave and S-wave moduli, and density), fracture (dry fracture weaknesses), porosity, and fluid (fluid bulk modulus). A Bayesian Markov chain Monte Carlo nonlinear inversion method is proposed to estimate fluid bulk modulus, porosity, and fracture weaknesses directly from azimuthal seismic data. The inversion method yields reasonable estimates in the case of synthetic data containing a moderate noise and stable results on real data. 相似文献
10.
Characterizing the pore space of rock samples using three‐dimensional (3D) X‐ray computed tomography images is a crucial step in digital rock physics. Indeed, the quality of the pore network extracted has a high impact on the prediction of rock properties such as porosity, permeability and elastic moduli. In carbonate rocks, it is usually very difficult to find a single image resolution which fully captures the sample pore network because of the heterogeneities existing at different scales. Hence, to overcome this limitation a multiscale analysis of the pore space may be needed. In this paper, we present a method to estimate porosity and elastic properties of clean carbonate (without clay content) samples from 3D X‐ray microtomography images at multiple resolutions. We perform a three‐phase segmentation to separate grains, pores and unresolved porous phase using 19 μm resolution images of each core plug. Then, we use images with higher resolution (between 0.3 and 2 μm) of microplugs extracted from the core plug samples. These subsets of images are assumed to be representative of the unresolved phase. We estimate the porosity and elastic properties of each sample by extrapolating the microplug properties to the whole unresolved phase. In addition, we compute the absolute permeability using the lattice Boltzmann method on the microplug images due to the low resolution of the core plug images. In order to validate the results of the numerical simulations, we compare our results with available laboratory measurements at the core plug scale. Porosity average simulations for the eight samples agree within 13%. Permeability numerical predictions provide realistic values in the range of experimental data but with a higher relative error. Finally, elastic moduli show the highest disagreements, with simulation error values exceeding 150% for three samples. 相似文献
11.
Michael K. Broadhead 《Geophysical Prospecting》2008,56(5):729-735
The Gassmann relations of poroelasticity provide a connection between the dry and the saturated elastic moduli of porous rock and are useful in a variety of petroleum geoscience applications. Because some uncertainty is usually associated with the input parameters, the propagation of error in the inputs into the final moduli estimates is immediately of interest. Two common approaches to error propagation include: a first-order Taylor series expansion and Monte-Carlo methods. The Taylor series approach requires derivatives, which are obtained either analytically or numerically and is usually limited to a first-order analysis. The formulae for analytical derivatives were often prohibitively complicated before modern symbolic computation packages became prevalent but they are now more accessible. We apply this method and present formulae for uncertainty in the predicted bulk and shear moduli for two forms of the Gassmann relations. Numerical results obtained with these uncertainty formulae are compared with Monte-Carlo calculations as a form of validation and to illustrate the relative characteristics of the two approaches. Particular emphasis is given to the problem of correlated variables, which are often ignored in naïve approaches to error analysis. Going out to the error level that the two methods were compared, the means agree and the variance of the Monte Carlo method for bulk modulus grows with input error. 相似文献
12.
The shales of the Qiongzhusi Formation and Wufeng–Longmaxi Formations at Sichuan Basin and surrounding areas are presently the most important stratigraphic horizons for shale gas exploration and development in China. However, the regional characteristics of the seismic elastic properties need to be better determined. The ultrasonic velocities of shale samples were measured under dry conditions and the relations between elastic properties and petrology were systemically analyzed. The results suggest that 1) the effective porosity is positively correlated with clay content but negatively correlated with brittle minerals, 2) the dry shale matrix consists of clays, quartz, feldspars, and carbonates, and 3) organic matter and pyrite are in the pore spaces, weakly coupled with the shale matrix. Thus, by assuming that all connected pores are only present in the clay minerals and using the Gassmann substitution method to calculate the elastic effect of organic matter and pyrite in the pores, a relatively simple rock-physics model was constructed by combining the self-consistent approximation (SCA), the differential effective medium (DEM), and Gassmann’s equation. In addition, the effective pore aspect ratio was adopted from the sample averages or estimated from the carbonate content. The proposed model was used to predict the P-wave velocities and generally matched the ultrasonic measurements very well. 相似文献
13.
The clay-sand mixture model of Xu and White is shown to simulate observed relationships between S-wave velocity (or transit time), porosity and clay content. In general, neither S-wave velocity nor S-wave transit time is a linear function of porosity and clay content. For practical purposes, clay content is approximated by shale volume in well-log applications. In principle, the model can predict S-wave velocity from lithology and any pair of P-wave velocity, porosity and shale volume. Although the predictions should be the same if all measurements are error free, comparison of predictions with laboratory and logging measurements show that predictions using P-wave velocity are the most reliable. The robust relationship between S- and P-wave velocities is due to the fact that both are similarly affected by porosity, clay content and lithology. Moreover, errors in the measured P-wave velocity are normally smaller than those in porosity and shale volume, both of which are subject to errors introduced by imperfect models and imperfect parameters when estimated from logs. Because the model evaluates the bulk and shear moduli of the dry rock frame by a combination of Kuster and Toksöz’ theory and differential effective medium theory, using pore aspect ratios to characterize the compliances of the sand and clay components, the relationship between P- and S-wave velocities is explicit and consistent. Consequently the model sidesteps problems and assumptions that arise from the lack of knowledge of these moduli when applying Gassmann's theory to this relationship, making it a very flexible tool for investigating how the vP-vs relationship is affected by lithology, porosity, clay content and water saturation. Numerical results from the model are confirmed by laboratory and logging data and demonstrate, for example, how the presence of gas has a more pronounced effect on P-wave velocity in shaly sands than in less compliant cleaner sandstones. 相似文献
14.
Elastic behaviour of North Sea chalk: A well-log study 总被引：1，自引：1，他引：0
L. Gommesen I.L. Fabricius T. Mukerji G. Mavko J.M. Pedersen 《Geophysical Prospecting》2007,55(3):307-322
We present two different elastic models for, respectively, cemented and uncemented North Sea chalk well‐log data. We find that low Biot coefficients correlate with anomalously low cementation factors from resistivity measurements at low porosity and we interpret this as an indication of cementation. In contrast, higher Biot coefficients and correspondingly higher cementation factors characterize uncemented chalk for the same (low) porosity. Accordingly, the Poisson's ratio–porosity relationship for cemented chalk is different from that of uncemented chalk. We have tested the application of the self‐consistent approximation, which here represents the unrelaxed scenario where the pore spaces of the rock are assumed to be isolated, and the Gassmann theory, which assumes that pore spaces are connected, as tools for predicting the effect of hydrocarbons from the elastic properties of brine‐saturated North Sea reservoir chalk. In the acoustic impedance–Poisson's ratio plane, we forecast variations in porosity and hydrocarbon saturation from their influence on the elastic behaviour of the chalk. The Gassmann model and the self‐consistent approximation give roughly similar predictions of the effect of fluid on acoustic impedance and Poisson's ratio, but we find that the high‐frequency self‐consistent approach gives a somewhat smaller predicted fluid‐saturation effect on Poisson's ratio than the low‐frequency Gassmann model. The Gassmann prediction for the near and potentially invaded zone corresponds more closely to logging data than the Gassmann prediction for the far, virgin zone. We thus conclude that the Gassmann approach predicts hydrocarbons accurately in chalk in the sonic‐frequency domain, but the fluid effects as recorded by the acoustic tool are significantly affected by invasion of mud filtrate. The amplitude‐versus‐angle (AVA) response for the general North Sea sequence of shale overlying chalk is predicted as a function of porosity and pore‐fill. The AVA response of both cemented and uncemented chalk generally shows a declining reflectivity coefficient versus offset and a decreasing normal‐incidence reflectivity with increasing porosity. However, for the uncemented model, a phase reversal will appear at a relatively lower porosity compared to the cemented model. 相似文献
15.
Larry Lines 《Geophysical Prospecting》2015,63(2):422-441
Unlike light oils, heavy oils do not have a well‐established scheme for modelling elastic moduli from dynamic reservoir properties. One of the main challenges in the fluid substitution of heavy oils is their viscoelastic nature, which is controlled by temperature, pressure, and fluid composition. Here, we develop a framework for fluid substitution modelling that is reliable yet practical for a wide range of cold and thermal recovery scenarios in producing heavy oils and that takes into account the reservoir fluid composition, grounded on the effective‐medium theories for estimating elastic moduli of an oil–rock system. We investigate the effect of fluid composition variations on oil–rock elastic moduli with temperature changes. The fluid compositional behaviour is determined by flash calculations. Elastic moduli are then determined using the double‐porosity coherent potential approximation method and the calculated viscosity based on the fluid composition. An increase in temperature imposes two opposing mechanisms on the viscosity behaviour of a heavy‐oil sample: gas liberation, which tends to increase the viscosity, and melting, which decreases the viscosity. We demonstrate that melting dominates gas liberation, and as a result, the viscosity and, consequently, the shear modulus of the heavy oils always decrease with increasing temperature. Furthermore, it turns out that one can disregard the effects of gas in the solution when modelling the elastic moduli of heavy oils. Here, we compare oil–rock elastic moduli when the rock is saturated with fluids that have different viscosity levels. The objective is to characterize a unique relation between the temperature, the frequency, and the elastic moduli of an oil–rock system. We have proposed an approach that takes advantage of this relation to find the temperature and, consequently, the viscosity in different regions of the reservoir. 相似文献
16.
Maxim Lebedev Moyra E.J. Wilson Vassily Mikhaltsevitch 《Geophysical Prospecting》2014,62(6):1253-1265
Petrophysical properties of carbonate reservoirs are less predictable than that of siliciclastic reservoirs. One of the main reasons for this is the physical and chemical interactions of carbonate rocks with pore fluids. Such interactions can significantly change the elastic properties of the rock matrix and grains, making the applicability of Gassmann's fluid substitution procedure debatable. This study is an attempt to understand the mechanisms of fluid‐rock interactions and the influence of these interactions on elastic parameters of carbonates. We performed precise indentation tests on Savonnières limestone at a microscale level under dry, distilled water, and n‐Decane saturated conditions. Our experiments display softening of the rock matrix after water saturation. We have found that mainly the ooid cortices, peloid nuclei and prismatic intergranular cement are affected by water flooding. We also observed a shear modulus reduction in Savonnières limestone in an experiment performed at ultrasonic frequencies. One of the most important results obtained in our experimental study is that the Gassmann fluid substitution theory might not always be applicable to predict the elastic moduli of fluid‐saturated limestones. 相似文献
17.
Ultrasonic compressional‐ and shear‐wave velocities have been measured on 34 samples of sandstones from hydrocarbon reservoirs. The sandstones are all of low clay content, high porosity, and cover a wide range of permeabilities. They were measured dry and brine‐saturated under hydrostatic effective stresses of 10, 20 and 40 MPa. For eight of the sandstones, ultrasonic velocity measurements were made at different partial water saturations in the range from dry to fully saturated. The Gassmann–Biot theory is found to account for most of the changes in velocities at high effective stress levels when the dry sandstones are fully saturated with brine, provided the lower velocities resulting when the dry sandstone initially adsorbs small amounts of moisture are used to determine the elastic properties of the ‘dry’ sandstone. At lower effective stress levels, local flow phenomena due to the presence of open microcracks are assumed to be responsible for measured velocities higher than those predicted by the theory. The partial saturation results are modelled fairly closely by the Gassmann–Biot theory, assuming heterogeneous saturation for P‐waves. 相似文献
18.
Mechanical compaction and ultrasonic velocity of sands with different texture and mineralogical composition 总被引：1，自引：0，他引：1
Manzar Fawad Nazmul Haque Mondol Jens Jahren Knut Bjørlykke 《Geophysical Prospecting》2011,59(4):697-720
This study presents the results of experimental compaction while measuring ultrasonic velocities of sands with different grain size, shape, sorting and mineralogy. Uniaxial mechanical compaction tests up to a maximum of 50 MPa effective stress were performed on 29 dry sand aggregates derived from eight different sands to measure the rock properties. A good agreement was found between the Gassmann saturated bulk moduli of dry and brine saturated tests of selected sands. Sand samples with poor sorting showed low initial porosity while sands with high grain angularity had high initial porosity. The sand compaction tests showed that at a given stress well‐sorted, coarse‐grained sands were more compressible and had higher velocities (Vp and Vs) than fine‐grained sands when the mineralogy was similar. This can be attributed to grain crushing, where coarser grains lead to high compressibility and large grain‐to‐grain contact areas result in high velocities. At medium to high stresses the angular coarse to medium grained sands (both sorted sands and un‐sorted whole sands) showed high compaction and velocities (Vp and Vs). The small grain‐to‐grain contact areas promote higher deformation at grain contacts, more crushing and increased porosity loss resulting in high velocities. Compaction and velocities (Vp and Vs) increased with decreasing sorting in sands. However, at the same porosity, the velocities in whole sands were slightly lower than in the well‐sorted sands indicating the presence of loose smaller grains in‐between the framework grains. Quartz‐poor sands (containing less than 55% quartz) showed higher velocities (Vp and Vs) compared to that of quartz‐rich sands. This could be the result of sintering and enlargement of grain contacts of ductile mineral grains in the quartz‐poor sands increasing the effective bulk and shear stiffness. Tests both from wet measurements and Gassmann brine substitution showed a decreasing Vp/Vs ratio with increasing effective stress. The quartz‐rich sands separated out towards the higher side of the Vp/Vs range. The Gassmann brine substituted Vp and Vs plotted against effective stress provide a measure of the expected velocity range to be found in these and similar sands during mechanical compaction. Deviations of actual well log data from experimental data may indicate uplift, the presence of hydrocarbon, overpressure and/or cementation. Data from this study may help to model velocity‐depth trends and to improve the characterization of reservoir sands from well log data in a low temperature (<80–100o C) zone where compaction of sands is mostly mechanical. 相似文献
19.
Computer simulations are used to calculate the elastic properties of model cemented sandstones composed of two or more mineral phases. Two idealized models are considered – a grain‐overlap clay/quartz mix and a pore‐lining clay/quartz mix. Unlike experimental data, the numerical data exhibit little noise yet cover a wide range of quartz/cement ratios and porosities. The results of the computations are in good agreement with experimental data for clay‐bearing consolidated sandstones. The effective modulus of solid mineral mixtures is found to be relatively insensitive to microstructural detail. It is shown that the Hashin–Shtrikman average is a good estimate for the modulus of the solid mineral mixtures. The distribution of the cement phase is found to have little effect on the computed modulus–porosity relationships. Numerical data for dry and saturated states confirm that Gassmann's equations remain valid for porous materials composed of multiple solid constituents. As noted previously, the Krief relationship successfully describes the porosity dependence of the dry shear modulus, and a recent empirical relationship provides a good estimate for the dry‐rock Poisson's ratio. From the numerical computations, a new empirical model, which requires only a knowledge of system mineralogy, is proposed for the modulus–porosity relationship of isotropic dry or fluid‐saturated porous materials composed of multiple solid constituents. Comparisons with experimental data for clean and shaly sandstones and computations for more complex, three‐mineral (quartz/dolomite/clay) systems show good agreement with the proposed model over a very wide range of porosities. 相似文献
20.
An inclusion model, based on the Kuster–Toksöz effective medium theory along with Gassmann theory, is tested to forward model velocities for fluid-saturated rocks. A simulated annealing algorithm, along with the inclusion model, effectively inverts measured compressional velocity (VP) to achieve an effective pore aspect ratio at each depth in a depth variant manner, continuously along with depth. Early Cretaceous syn-rift clastic sediments at two different depth intervals from two wells [well A (2160–2274 m) and well B (5222–5303 m)], in the Krishna–Godavari basin, India, are used for this study. Shear velocity (VS) estimated using modelled pore aspect ratio offers a high correlation coefficient (>0.95 for both the wells) with measured data. The modelled pore aspect ratio distribution suggests the decrease in pore aspect ratio for the deeper interval, mainly due to increased effective vertical stress. The pore aspect ratio analysis in relation to total porosity and volume of clay reveals that the clay volume has insignificant influence in shaping the pore geometry in the studied intervals. An approach based on multiple linear regression method effectively predicts velocity as a linear function of total porosity, the volume of clay and the modelled pore-space aspect ratio of the rock. We achieved a significant match between measured and predicted velocities. The correlation coefficients between measured and modelled velocities are considerably high (approximately 0.85 and 0.8, for VP and VS, respectively). This process indicates the possible influence of pore geometry along with total porosity and volume of clay on velocity. 相似文献