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.     

Influence of pore pressure on velocity in low-porosity sandstone: Implications for time-lapse feasibility and pore-pressure study

As seismic data quality improves, time‐lapse seismic data is increasingly being called upon to interpret and predict changes during reservoir development and production. Since pressure change is a major component of reservoir change during production, a thorough understanding of the influence of pore pressure on seismic velocity is critical. Laboratory measurements show that differential pressure (overburden minus fluid pressure) does not adequately determine the actual reservoir conditions. Changes in fluid pressure are found to have an additional effect on the physical properties of rocks. The effective‐stress coefficient n is used to quantify the effect of pore pressure compared to confining pressure on rock properties. However, the current practice in time‐lapse feasibility studies, reservoir‐pressure inversion and pore‐pressure prediction is to assume that n= 1. Laboratory measurements, reported in both this and previous research show that n can be significantly less than unity for low‐porosity rocks and that it varies with porosity, rock texture and wave type. We report the results of ultrasonic experiments to estimate n for low‐porosity sandstones with and without microcracks. Our results show that, for P‐waves, n is as low as 0.4 at a differential pressure of 20 MPa (about 3000 psi) for a low‐porosity sandstone. Thus, in pore‐pressure inversion, an assumption of n= 1 would lead to a 150% underestimation of the pore pressure. Comparison of the effective‐stress coefficient for fractured and unfractured samples suggests that the presence of microfractures increases the sensitivity of P‐wave velocity to pore pressure, and therefore the effective‐stress coefficient. Our results show that the effective‐stress coefficient decreases with the differential pressure, with a higher differential pressure resulting in a lower effective‐stress coefficient. While the effective‐stress coefficient for P‐wave velocity can be significantly less than unity, it is close to one for S‐waves.     

SHEAR-WAVE VELOCITY ESTIMATION IN POROUS ROCKS: THEORETICAL FORMULATION,PRELIMINARY VERIFICATION AND APPLICATIONS1

Shear-wave velocity logs are useful for various seismic interpretation applications, including bright spot analyses, amplitude-versus-offset analyses and multicomponent seismic interpretations. Measured shear-wave velocity logs are, however, often unavailable. We developed a general method to predict shear-wave velocity in porous rocks. If reliable compressional-wave velocity, lithology, porosity and water saturation data are available, the precision and accuracy of shear-wave velocity prediction are 9% and 3%, respectively. The success of our method depends on: (1) robust relationships between compressional- and shear-wave velocities for water-saturated, pure, porous lithologies; (2) nearly linear mixing laws for solid rock constituents; (3) first-order applicability of the Biot–Gassmann theory to real rocks. We verified these concepts with laboratory measurements and full waveform sonic logs. Shear-wave velocities estimated by our method can improve formation evaluation. Our method has been successfully tested with data from several locations.     

Attenuation of P- and S-waves in limestones

Ultrasonic compressional- and shear-wave attenuation measurements have been made on 40, centimetre-sized samples of water- and oil-saturated oolitic limestones at 50 MPa effective hydrostatic pressure (confining pressure minus pore-fluid pressure) at frequencies of about 0.85 MHz and 0.7 MHz respectively, using the pulse-echo method. The mineralogy, porosity, permeability and the distribution of the pore types of each sample were determined using a combination of optical and scanning electron microscopy, a helium porosimeter and a nitrogen permeameter. The limestones contain a complex porosity system consisting of interparticle macropores (dimensions up to 300 microns) and micropores (dimensions 5–10 microns) within the ooids, the calcite cement and the mud matrix. Ultrasonic attenuation reaches a maximum value in those limestones in which the dual porosity system is most fully developed, indicating that the squirt-flow mechanism, which has previously been shown to occur in shaley sandstones, also operates in the limestones. It is argued that the larger-scale dual porosity systems present in limestones in situ could similarly cause seismic attenuation at the frequencies of field seismic surveys through the operation of the squirt-flow mechanism.     

Ultrasonic wave propagation in dry and brine-saturated sandstones as a function of effective stress: laboratory measurements and modelling1

Compressional and shear-wave velocities have been measured and a novel approach using digital processing employed to study wave attenuation for brine- and gas- saturated sandstones, over a range of effective stresses from 5 to 60 MPa. Also measured were the complex conductivity in the brine-saturated state and permeability in the gas-saturated state over the same range of stresses as for the velocity measurements. Broadband ultrasonic pulses of P- and orthogonally polarized S-waves in the frequency range 0.3–0.8 MHz are transmitted through the specimen to be characterized for comparison with a reference (aluminium) having low attenuation. The attenuation is calculated in terms of the quality factor Q from the Fourier spectral ratios, using the frequency spectral ratios technique. The corrections necessary for the effects of diffraction due to the finite size of the ultrasonic transducers have been carried out for the case of measurements under lower confining stress. To interpret the laboratory measured velocity and attenuation data under the physical conditions of this study and to estimate the effects of pore structure, numerical modelling of velocities and attenuation as functions of the confining stress have been performed, based on the MIT model. Theoretical models based on several hypothesized attenuation mechanisms are considered in relation to laboratory data of the effects of confining pressure, fluid saturation and pore structure on attenuation. Numerical calculations using these models with the experimental data indicate that friction on thin cracks and grain boundaries is the dominant attenuation mechanism for dry and brine-saturated sandstones at low effective stresses for the frequencies tested. However, for brine-saturated sandstones at moderately high effective stresses, fluid flow could play a more important role in ultrasonic S-wave attenuation, depending on the pore structure of the sample.     

Biot dispersion for P‐ and S‐wave velocities in partially and fully saturated sandstones

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.     

Comparison of stress-dependent geophysical,hydraulic and mechanical properties of synthetic and natural sandstones for reservoir characterization and monitoring studies

Synthetic rock samples can offer advantages over natural rock samples when used for laboratory rock physical properties studies, provided their success as natural analogues is well understood. The ability of synthetic rocks to mimic the natural stress dependency of elastic wave, electrical and fluid transport properties is of primary interest. Hence, we compare a consistent set of laboratory multi-physics measurements obtained on four quartz sandstone samples (porosity range 20–25%) comprising two synthetic and two natural (Berea and Corvio) samples, the latter used extensively as standards in rock physics research. We measured simultaneously ultrasonic (P- and S-wave) velocity and attenuation, electrical resistivity, permeability and axial and radial strains over a wide range of differential pressure (confining stress 15–50 MPa; pore pressure 5–10 MPa) on the four brine saturated samples. Despite some obvious physical discrepancies caused by the synthetic manufacturing process, such as silica cementation and anisotropy, the results show only small differences in stress dependency between the synthetic and natural sandstones for all measured parameters. Stress dependency analysis of the dry samples using an isotropic effective medium model of spheroidal pores and penny-shaped cracks, together with a granular cohesion model, provide evidence of crack closure mechanisms in the natural sandstones, seen to a much lesser extent in the synthetic sandstones. The smaller grain size, greater cement content, and cementation under oedometric conditions particularly affect the fluid transport properties of the synthetic sandstones, resulting in lower permeability and higher electrical resistivity for a similar porosity. The effective stress coefficients, determined for each parameter, are in agreement with data reported in the literature. Our results for the particular synthetic materials that were tested suggest that synthetic sandstones can serve as good proxies for natural sandstones for studies of elastic and mechanical properties, but should be used with care for transport properties studies.     

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.     

含流体砂岩地震波频散实验研究

为了研究孔隙流体对不同渗透率岩石地震波速度的影响,在实验室利用跨频带岩石弹性参数测试系统得到了应变幅值10-6的2~2000Hz频段下的地震波速度和1 MHz频率下的超声波速度,利用差分共振声谱法得到了频率600Hz岩石干燥和完全饱水情况下岩石声学参数.实验表明,在低饱和度下,致密砂岩在地震和超声频段下没有明显的频散;在高饱和度下纵波速度的频散变得明显.从干燥到完全水饱和条件,不同频率测量的致密砂岩的体积模量随岩石孔隙度增高而降低,且体积模量的变化量受岩石微观孔隙结构的影响较大.高孔、高渗砂岩无论在低含水度下还是在高含水饱和度下频散微弱,并且在地震频段下围压对于岩石纵横波速度的影响要大于频率的影响.高孔、高渗砂岩和致密砂岩不同含水饱和度下的频散差异可应用于储层预测,油气检测等方面,同时该研究可以更好地帮助理解岩石的黏弹性行为,促进岩石物理频散理论的发展,提高地震解释的精度.     

VISCOELASTIC SEISMIC RESPONSES OF 2D RESERVOIR MODELS1

The use of relaxation mechanisms has recently made it possible to simulate viscoelastic (Q) effects accurately in time-domain numerical computations of seismic responses. As a result, seismograms may now be synthesized for models with arbitrary spatial variations in compressional- and shear-wave quality factors (Q₉, and Q_s, as well as in density (ρ) and compressional- and shear-wave velocities (V_p, and V_s). Reflections produced by Q contrasts alone may have amplitudes as large as those produced by velocity contrasts. Q effects, including their interaction with V_p, V_s and p, contribute significantly to the seismic response of reservoirs. For band-limited data at typical seismic frequencies, the effects of Q on reflectivity and attenuation are more visible than those on dispersion. Synthetic examples include practical applications to reservoir exploration, evaluation and monitoring. Q effects are clearly visible in both surface and offset vertical seismic profile data. Thus, AVO analyses that neglect Q may produce erroneous conclusions.     

Controls on sonic velocity in carbonates

Compressional and shear-wave velocities (V _p andV _s) of 210 minicores of carbonates from different areas and ages were measured under variable confining and pore-fluid pressures. The lithologies of the samples range from unconsolidated carbonate mud to completely lithified limestones. The velocity measurements enable us to relate velocity variations in carbonates to factors such as mineralogy, porosity, pore types and density and to quantify the velocity effects of compaction and other diagenetic alterations.Pure carbonate rocks show, unlike siliciclastic or shaly sediments, little direct correlation between acoustic properties (V _p andV _s) with age or burial depth of the sediments so that velocity inversions with increasing depth are common. Rather, sonic velocity in carbonates is controlled by the combined effect of depositional lithology and several post-depositional processes, such as cementation or dissolution, which results in fabrics specific to carbonates. These diagenetic fabrics can be directly correlated to the sonic velocity of the rocks.At 8 MPa effective pressureV _p ranges from 1700 to 6500 m/s, andV _s ranges from 800 to 3400 m/s. This range is mainly caused by variations in the amount and type of porosity and not by variations in mineralogy. In general, the measured velocities show a positive correlation with density and an inverse correlation with porosity, but departures from the general trends of correlation can be as high as 2500 m/s. These deviations can be explained by the occurrence of different pore types that form during specific diagenetic phases. Our data set further suggests that commonly used correlations like Gardner's Law (V _p-density) or the time-average-equation (V _p-porosity) should be significantly modified towards higher velocities before being applied to carbonates.The velocity measurements of unconsolidated carbonate mud at different stages of experimental compaction show that the velocity increase due to compaction is lower than the observed velocity increase at decreasing porosities in natural rocks. This discrepancy shows that diagenetic changes that accompany compaction influence velocity more than solely compaction at increasing overburden pressure.The susceptibility of carbonates to diagenetic changes, that occur far more quickly than compaction, causes a special velocity distribution in carbonates and complicates velocity estimations. By assigning characteristic velocity patterns to the observed diagenetic processes, we are able to link sonic velocity to the diagenetic stage of the rock.     

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.     

汶川地震破裂带断层岩纵波速度与孔隙度关系的实验研究

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（V_p）和总孔隙度（φ_t）进行了测量,并深入分析了V_p与孔隙度的关系.结果表明在10~600 MPa的压力范围内,V_p（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∂V_p（p）/∂p=a_v/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V_p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.     

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.     

Effective medium theory and multiple linear regression-based velocity estimation in syn-rift clastic sequence of the Krishna–Godavari basin,India

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 (V_P) 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 (V_S) 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 V_P and V_S, respectively). This process indicates the possible influence of pore geometry along with total porosity and volume of clay on velocity.     

The stress sensitivity of shaley sandstones

The link between the stress sensitivity of shaley sandstones and their porosity and clay content is investigated. This is achieved by firstly fitting a compliance‐based stress‐sensitivity law to laboratory measurements of ultrasonic velocity taken from four sets of reservoir sandstones, extracted from a variety of depositional settings. Correlations are then sought between the independent parameters of this law and the porosity or clay fraction of the rocks, which are then subsequently interpreted in terms of framework or pore‐space‐related microstructural clay models. The general conclusion drawn from the results is that both of the parameters defining the stress‐sensitivity law (the asymptotic modulus and the stress‐dependent excess compliance) clearly vary with porosity. However, only the asymptotic modulus shows a convincing trend with clay and there is little observed variation of the stress‐dependent compliance with clay. There is therefore a resultant variation of stress sensitivity with clay, but it is controlled only by the asymptotic modulus. The analysis also concludes that all four data sets fall into a framework‐related category of clay model.     

INTEGRATED INTERPRETATION OF MARINE ENGINEERING GEOLOGICAL AND GEOPHYSICAL DATA ON THE PRINCIPLES OF EXPERT SYSTEM TECHNOLOGY1

We describe an approach to the construction of an engineering geological expert system for identification of sub-bottom soils in accordance with some predefined nomenclature. The following principles of integrated interpretation of engineering geophysical and geotechnical data are presented: Firstly, the transformation of physical data (compressional- and shear-wave velocities, compressional-wave attenuation coefficients, electrical conductivity, etc.) for each of the medium points into subjective probabilities for the soil belonging to each type listed in the nomenclature, and secondly, the extrapolation of local geotechnical data (primarily drilling data) to the surrounding space by means of diffusion of the initial membership function distribution, resulting in the same set of probabilities for soil types at each point in the medium under consideration. Aggregation of the fuzzy information obtained, sufficient for reaching a conclusion for most points in the medium, is carried out by means of Bayesian summation. An example is given of integrated interpretation of real data obtained from four different sources (compressional- and shear-wave velocity sections V_p(x, z) and V_s(x, z), and two boreholes) related to the same profile.     

Ultrasonic velocities of North Sea chalk samples: influence of porosity, fluid content and texture

We have studied 56 unfractured chalk samples of the Upper Cretaceous Tor Formation of the Dan, South Arne and Gorm Fields, Danish North Sea. The samples have porosities of between 14% and 45% and calcite content of over 95%. The ultrasonic compressional‐ and shear‐wave velocities (V_P and V_S) for dry and water‐saturated samples were measured at up to 75 bar confining hydrostatic pressure corresponding to effective stress in the reservoir. The porosity is the main control of the ultrasonic velocities and therefore of the elastic moduli. The elastic moduli are slightly higher for samples from the South Arne Field than from the Dan Field for identical porosities. This difference may be due to textural differences between the chalk at the two locations because we observe that large grains (i.e. filled microfossils and fossil fragments) that occur more frequently in samples from the Dan Field have a porosity‐reducing effect and that samples rich in large grains have a relatively low porosity for a given P‐wave modulus. The clay content in the samples is low and is mainly represented by either kaolinite or smectite; samples with smectite have a lower P‐wave modulus than samples with kaolinite at equal porosity. We find that ultrasonic V_P and V_S of dry chalk samples can be satisfactorily estimated with Gassmann's relationships from data for water‐saturated samples. A pronounced difference between the V_P/V_S ratios for dry and water‐saturated chalk samples indicates promising results for seismic amplitude‐versus‐offset analyses.     

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.     

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.