The effect of clay distribution on the elastic properties of sandstones

The shape and location of clay within sandstones have a large impact on the P‐wave and S‐wave velocities of the rock. They also have a large effect on reservoir properties and the interpretation of those properties from seismic data and well logs. Numerical models of different distributions of clay – structural, laminar and dispersed clay – can lead to an understanding of these effects. Clay which is located between quartz grains, structural clay, will reduce the P‐wave and S‐wave velocities of the rock. If the clay particles become aligned or form layers, the velocities perpendicular to the alignment will be reduced further. S‐wave velocities decrease more rapidly than P‐wave velocities with increasing clay content, and therefore Poisson's ratios will increase as the velocities decrease. These effects are more pronounced for compacted sandstones. Small amounts of clay that are located in the pore space will have little effect on the P‐wave velocity due to the competing influence of the density effect and pore‐fluid stiffening. The S‐wave velocity will decrease due to the density effect and thus the Poisson's ratio will increase. When there is sufficient clay to bridge the gaps between the quartz grains, P‐wave and S‐wave velocities rise rapidly and the Poisson's ratios decrease. These effects are more pronounced for under‐compacted sandstones. These general results are only slightly modified when the intrinsic anisotropy of the clay material is taken into account. Numerical models indicate that there is a strong, nearly linear relationship between P‐wave and S‐wave velocity which is almost independent of clay distribution. S‐wave velocities can be predicted reasonably accurately from P‐wave velocities based on empirical relationships. However, this does not provide any connection between the elastic and petrophysical properties of the rocks. Numerical modelling offers this connection but requires the inclusion of clay distribution and anisotropy to provide a model that is consistent with both the elastic and petrophysical properties. If clay distribution is ignored, predicting porosities from P‐wave or S‐wave data, for example, can result in large errors. Estimation of the clay distribution from P‐wave and S‐wave velocities requires good estimates of the porosity and clay volume and verification from petrographic analyses of core or cuttings. For a real data example, numerical models of the elastic properties suggest the predominance of dispersed clay in a fluvial sand from matching P‐wave and S‐wave velocity well log data using log‐based estimates of the clay volume and porosity. This is consistent with an interpretation of other log data.     

Joint elastic‐electrical properties of reservoir sandstones and their relationships with petrophysical parameters

We measured in the laboratory ultrasonic compressional and shear‐wave velocity and attenuation (0.7–1.0 MHz) and low‐frequency (2 Hz) electrical resistivity on 63 sandstone samples with a wide range of petrophysical properties to study the influence of reservoir porosity, permeability and clay content on the joint elastic‐electrical properties of reservoir sandstones. P‐ and S‐wave velocities were found to be linearly correlated with apparent electrical formation factor on a semi‐logarithmic scale for both clean and clay‐rich sandstones; P‐ and S‐wave attenuations showed a bell‐shaped correlation (partial for S‐waves) with apparent electrical formation factor. The joint elastic‐electrical properties provide a way to discriminate between sandstones with similar porosities but with different clay contents. The laboratory results can be used to estimate sandstone reservoir permeability from seismic velocity and apparent formation factor obtained from co‐located seismic and controlled source electromagnetic surveys.     

A semi-empirical velocity-porosity-clay model for petrophysical interpretation of P- and S-velocities

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.     

A generalized Biot–Gassmann model for the acoustic properties of shaley sandstones1

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.     

油藏水驱开采时移地震监测岩石物理基础测量

岩石物理测量是油藏水驱开采时移地震监测的基础.在实验室对来自胜利油田的5块岩石样品模拟储层条件进行了水驱和气驱动态岩石物理弹性测量,重点分析了流体替换、温度、孔隙压力对岩石纵、横波速度的影响.实验表明,在水驱情形下,由于流体替换和温度、孔隙压力变化所引起的岩石纵横波速度的变化均很小,实施时移地震监测具有较大的风险性.相比之下,气驱可能引起较为明显的纵波速度变化,有利于时移地震监测的实施.进一步完善实验方法、丰富实验内容、是今后时移地震岩石物理实验研究的主要任务.     

Velocities of compressional and shear waves in limestones

Carbonate rocks are important hydrocarbon reservoir rocks with complex textures and petrophysical properties (porosity and permeability) mainly resulting from various diagenetic processes (compaction, dissolution, precipitation, cementation, etc.). These complexities make prediction of reservoir characteristics (e.g. porosity and permeability) from their seismic properties very difficult. To explore the relationship between the seismic, petrophysical and geological properties, ultrasonic compressional‐ and shear‐wave velocity measurements were made under a simulated in situ condition of pressure (50 MPa hydrostatic effective pressure) at frequencies of approximately 0.85 MHz and 0.7 MHz, respectively, using a pulse‐echo method. The measurements were made both in vacuum‐dry and fully saturated conditions in oolitic limestones of the Great Oolite Formation of southern England. Some of the rocks were fully saturated with oil. The acoustic measurements were supplemented by porosity and permeability measurements, petrological and pore geometry studies of resin‐impregnated polished thin sections, X‐ray diffraction analyses and scanning electron microscope studies to investigate submicroscopic textures and micropores. It is shown that the compressional‐ and shear‐wave velocities (V_p and V_s, respectively) decrease with increasing porosity and that V_p decreases approximately twice as fast as V_s. The systematic differences in pore structures (e.g. the aspect ratio) of the limestones produce large residuals in the velocity versus porosity relationship. It is demonstrated that the velocity versus porosity relationship can be improved by removing the pore‐structure‐dependent variations from the residuals. The introduction of water into the pore space decreases the shear moduli of the rocks by about 2 GPa, suggesting that there exists a fluid/matrix interaction at grain contacts, which reduces the rigidity. The predicted Biot–Gassmann velocity values are greater than the measured velocity values due to the rock–fluid interaction. This is not accounted for in the Biot–Gassmann velocity models and velocity dispersion due to a local flow mechanism. The velocities predicted by the Raymer and time‐average relationships overestimated the measured velocities even more than the Biot model.     

Pressure effects on the joint elastic‐electrical properties of reservoir sandstones

We conducted a laboratory study of the joint elastic‐electrical properties of sixty‐three brine‐saturated sandstone samples to assess the likely impact of differential pressure (confining minus pore fluid pressures) in the range 8–60 MPa on the joint interpretation of marine seismic and controlled‐source electromagnetic survey data. The samples showed a wide range of petrophysical properties representative of most sandstone reservoirs. We found that a regression equation comprising both a constant and an exponential part gave a good fit to the pressure dependence of all five measured geophysical parameters (ultrasonic P‐ and S‐wave velocity, attenuation and electrical resistivity). Electrical resistivity was more pressure‐sensitive in clay‐rich sandstones with higher concentrations of low aspect ratio pores and micropores than in clean sandstones. Attenuation was more pressure‐sensitive in clean sandstones with large open pores (macropores) than in clay‐rich sandstones. Pore shape did not show any influence on the pressure sensitivity of elastic velocity. As differential pressure increases, the effect of the low aspect ratio pores and micropores on electrical resistivity becomes stronger than the effect of the macropores on attenuation. Further analysis of correlations among the five parameters as a function of pressure revealed potentially diagnostic relationships for geopressure prediction in reservoir sandstones.     

A physical model for shear-wave velocity prediction1

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 v_P-v_s 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.     

基于储层砂岩微观孔隙结构特征的弹性波频散响应分析

储层砂岩微观孔隙结构特征不仅影响干燥岩石的弹性波传播速度,也决定了岩石介质中与流体流动相关的速度频散与衰减作用.依据储层砂岩微观结构特征及速度随有效压力变化的非线性特征,将其孔隙体系理想化为不同形状的硬孔隙(纵横比α0.01)与软孔隙(纵横比α0.01)的组合(双孔隙结构).基于孔弹性理论,给出软孔隙最小初始纵横比值(一定压力下所有未闭合软孔隙在零压力时的纵横比最小值)的解析表达式,并在此基础上利用岩石速度-压力实验观测结果给出求取介质中两类孔隙纵横比及其含量分布特征的方法.通过逐步迭代加入软孔隙的方法对基于特征纵横比的"喷射流"(squirt fluid)模型进行了扩展,以考虑复杂孔隙分布特征对岩石喷射流作用的影响及其可能引起的速度频散特征.相较于典型的喷射流作用速度频散模式,对于岩石中软孔隙纵横比及其对应含量在较宽的范围呈谱分布的一般情况,其速度频散曲线不存在明显的低频段和中间频段,速度随频率的增大呈递增趋势直至高频极限.这说明即使在地震频段,微观尺度下的喷射流作用仍起一定作用,同样会造成流体饱和岩石介质的地震速度与Gassmann方程预测结果有不可忽略的差异.本文是对现有喷射流模型的重要补充,也为利用实验数据建立不同频段间岩石弹性波传播速度的可能联系提供了理论依据.     

Field velocity resistivity probe for estimating stiffness and void ratio

Elastic and electromagnetic waves are commonly used to investigate various soil characteristics. The goal of this study is to estimate the elastic moduli and the void ratio based on both the compressional and shear wave velocities, and the electrical resistivity measured by field velocity resistivity probe (FVRP). The compressional and shear waves are measured by piezoelectric disk elements and bender elements installed at the end of the FVRP frame tip. The electrical resistivity is determined by the electrical resistivity probe installed at the tip of the FVRP frame. The FVRP tests are carried out in a clay–sand mixture prepared in a calibration chamber and in silty sand to silty clay soils in the field. The elastic waves and electrical resistivity are measured at every 1 cm. The field tests are carried out at a depth of 6–20 m, at 10 cm intervals, at the Southern coastal area of the Korean peninsula. The measured data are converted into the constraint and shear moduli based on the elastic waves. Void ratios are evaluated based on the elastic wave velocities and the electrical resistivity, and these void ratios match the volumetric void ratio well. This study suggests that the FVRP may effectively determine the elastic moduli and void ratio.     

储层弹性与物性参数地震叠前同步反演的确定性优化方法

储层弹性与物性参数可直接应用于储层岩性预测和流体识别,是储层综合评价和油气藏精细描述的基本要素之一.现有的储层弹性与物性参数地震同步反演方法大都基于Gassmann方程,使用地震叠前数据,通过随机优化方法反演储层弹性与物性参数;或基于Wyllie方程,使用地震叠后数据,通过确定性优化方法反演储层弹性与物性参数.本文提出一种基于Gassmann方程、通过确定性优化方法开展储层弹性和物性参数地震叠前反演的方法,该方法利用Gassmann方程建立储层物性参数与叠前地震观测数据之间的联系,在贝叶斯反演框架下以储层弹性与物性参数的联合后验概率为目标函数,通过将目标函数的梯度用泰勒公式展开得到储层弹性与物性参数联合的方程组,其中储层弹性参数对物性参数的梯度用差分形式表示,最后通过共轭梯度算法迭代求解得到储层弹性与物性参数的最优解.理论试算与实际资料反演结果证明了方法的可行性.     

How does water near clay mineral surfaces influence the rock physics of shales?

Clays and clay‐bearing rocks like shale are extremely water sensitive. This is partly due to the interaction between water and mineral surfaces, strengthened by the presence of nanometer‐size pores and related large specific surface areas. Molecular‐scale numerical simulations, using a discrete‐element model, show that shear rigidity can be associated with structurally ordered (bound or adsorbed) water near charged surfaces. Building on these and other molecular dynamics simulations plus nanoscale experiments from the literature, the water monolayer adjacent to hydrophilic solid surfaces appears to be characterised by shear stiffness and/or enhanced viscosity. In both cases, elastic wave propagation will be affected by the bound or adsorbed water. Using a simple rock physics model, bound water properties were adjusted to match laboratory measured P‐ and S‐wave velocities on pure water‐saturated kaolinite and smectite. To fit the measured stress sensitivity, particularly for kaolinite, the contribution from solid‐grain contact stiffness needs to be added. The model predicts, particularly for S‐waves, that viscoelastic bound water could be a source of dispersion in clay and clay‐rich rocks. The bound‐water‐based rock physics model is found to represent a lower bound to laboratory‐measured velocities obtained with shales of different mineralogy and porosity levels.     

Comparison of infiltration models

Fourteen popular, representative infiltration models, some physically based, some semi‐empirical and some empirical, were selected for a comparative evaluation. Using the Nash and Sutcliffe efficiency criterion, the models were evaluated and compared for 243 sets of infiltration data collected from field and laboratory tests conducted in India and the USA on soils ranging from coarse sand to fine clay. Based on a relative grading scale, the semi‐empirical Singh–Yu general model, Holtan model and Horton model were graded respectively as 6·52, 5·57 and 5·48 out of 10. The empirical Huggins and Monke model, modified Kostiakov and Kostiakov model were graded as 5·57, 5·30 and 5·22, respectively. The physically based non‐linear and linear models of Smith–Parlange were graded as 5·48 and 5·22, respectively. Other models were ranked lower than these models. All the models generally performed poorly in field tests on Georgia's sandy soils, except the Robertsdale loamy sand. Copyright © 2003 John Wiley & Sons, Ltd.     

The porosity of saturated shallow sediments from seismic compressional and shear wave velocities

This study devises a new analytical relationship to determine the porosity of water-saturated soils at shallow depth using seismic compressional and shear wave velocities. Seismic refraction surveys together with soil sample collection were performed in selected areas containing water-saturated clay–silt, sand and gravely soils. Classification of clay–silt, sand and gravel dense soils provided the coefficient of experimental equation between the data sets, namely, Poisson's ratio, shear modulus and porosity values. This study presents a new analytical relationship between Poisson's ratio and shear modulus values, which are obtained from seismic velocities and porosity values of water-saturated material computed from water content and grain densities, which are determined by laboratory analysis of disturbed samples. The analytical relationship between data sets indicates that when the shear modulus of water-saturated loose soil increases, porosity decreases logarithmically. If shear modulus increases in dense or solid saturated soils, porosity decreases linearly.     

Seismic characterization of vertical fractures described as general linear-slip interfaces

Fluid flow in many hydrocarbon reservoirs is controlled by aligned fractures which make the medium anisotropic on the scale of seismic wavelength. Applying the linear‐slip theory, we investigate seismic signatures of the effective medium produced by a single set of ‘general’ vertical fractures embedded in a purely isotropic host rock. The generality of our fracture model means the allowance for coupling between the normal (to the fracture plane) stress and the tangential jump in displacement (and vice versa). Despite its low (triclinic) symmetry, the medium is described by just nine independent effective parameters and possesses several distinct features which help to identify the physical model and estimate the fracture compliances and background velocities. For example, the polarization vector of the vertically propagating fast shear wave S₁ and the semi‐major axis of the S₁‐wave normal‐moveout (NMO) ellipse from a horizontal reflector always point in the direction of the fracture strike. Moreover, for the S₁‐wave both the vertical velocity and the NMO velocity along the fractures are equal to the shear‐wave velocity in the host rock. Analysis of seismic signatures in the limit of small fracture weaknesses allows us to select the input data needed for unambiguous fracture characterization. The fracture and background parameters can be estimated using the NMO ellipses from horizontal reflectors and vertical velocities of P‐waves and two split S‐waves, combined with a portion of the P‐wave slowness surface reconstructed from multi‐azimuth walkaway vertical seismic profiling (VSP) data. The stability of the parameter‐estimation procedure is verified by performing non‐linear inversion based on the exact equations.     

Estimation of clay content in soil based on resistivity modelling and laboratory measurements

The determination of clay content in near‐surface formations is crucial for geotechnical, hydrogeological and oil‐contamination studies. We have developed a technique for estimating clay content that consists of the minimization of the difference between the theoretically calculated and measured soil resistivities as a function of water salinity. To calculate the resistivity, we used a model that takes into account the electrochemical processes in the clay micropores. The experimental measurements of soil resistivity were performed on soil samples, completely saturated by brines at different concentrations of NaCl salt in the range 0.6–100 g/l, to obtain the resistivity versus salinity curve. The parameters obtained with this curve inversion are the clay content, the total porosity and the cation exchange capacity. To verify the new technique, we determined clay concentrations of artificial mixtures of calibrated sand and clay. The relative mean error in the clay content does not exceed 20% for a 5% fitting error of the resistivity versus salinity curves. Such evaluations allow the correct separation of the main lithological groups (sand, sandy loam, loam, and light, medium and heavy clay). We applied this technique to estimate the petrophysical parameters of soils (clay content, porosity and cation exchange capacity) at various sites in Mexico. The results improved the interpretation of the vertical electrical soundings, the lithological soil characterization and the delineation of oil‐contaminated areas.     

基于统计岩石物理模型的各向异性页岩储层参数反演

提出了各向异性页岩储层统计岩石物理反演方法.通过统计岩石物理模型建立储层物性参数与弹性参数的定量关系,使用测井数据及井中岩石物理反演结果作为先验信息,将地震阻抗数据定量解释为储层物性参数、各向异性参数的空间分布.反演过程在贝叶斯框架下求得储层参数的后验概率密度函数,并从中得到参数的最优估计值及其不确定性的定量描述.在此过程中综合考虑了岩石物理模型对复杂地下介质的描述偏差和地震数据中噪声对反演不确定性的影响.在求取最大后验概率过程中使用模拟退火优化粒子群算法以提高收敛速度和计算准确性.将统计岩石物理技术应用于龙马溪组页岩气储层,得到储层泥质含量、压实指数、孔隙度、裂缝密度等物性,以及各向异性参数的空间分布及相应的不确定性估计,为页岩气储层的定量描述提供依据.     

用岩芯模拟测试参数做模型正演预测储层油、气、水边界

利用地震资料进行AVO油气检测,需要提供准确的储层岩石物性参数．通过对准噶尔盆地西部储层岩样实验室测定,得出合不同流体岩石在不同温度、压力下纵横波速度、速度比、泊松比的变化规律及差异．根据其差异性,用Zoeppritz方程做模型正演,以确定目的层有无AVO响应,以便对地震剖面做针对性的特殊处理．实际应用结果表明,用实验室测试的岩石物性参数做模型正演,可提高AVO检测的准确性,为用地震资料结合实验室岩芯测试参数预测地层油、气、水边界提供了有效手段．     

Joint elastic‐electrical effective medium models of reservoir sandstones

Improvements in the joint inversion of seismic and marine controlled source electromagnetic data sets will require better constrained models of the joint elastic‐electrical properties of reservoir rocks. Various effective medium models were compared to a novel laboratory data set of elastic velocity and electrical resistivity (obtained on 67 reservoir sandstone samples saturated with 35 g/l brine at a differential pressure of 8 MPa) with mixed results. Hence, we developed a new three‐phase effective medium model for sandstones with pore‐filling clay minerals based on the combined self‐consistent approximation and differential effective medium model. We found that using a critical porosity of 0.5 and an aspect ratio of 1 for all three components, the proposed model gave accurate model predictions of the observed magnitudes of P‐wave velocity and electrical resistivity and of the divergent trends of clean and clay‐rich sandstones at higher porosities. Using only a few well‐constrained input parameters, the new model offers a practical way to predict in situ porosity and clay content in brine saturated sandstones from co‐located P‐wave velocity and electrical resistivity data sets.     

山西大同市区剪切波速与土层岩性及深度关系的研究

在对山西大同市区3个主要地貌单元共72个钻孔的剪切波速资料分析整理的基础上,利用指数形式的剪切波速与深度经验公式,对测点较多的粉质黏土、粉土、粗砂三类土层的剪切波速Vs与土层深度H的关系进行统计回归,并将实测剪切波速值与利用上述统计结果得到的预测值进行对比检验,结果表明,分地貌单元各类土层的Vs-H经验关系是可靠的,符合当地岩土特征,可用于对该地区地层剪切波速进行推测。