Modelling elastic properties of impure chalk from South Arne Field, North Sea

In impure chalk, the elastic moduli are not only controlled by porosity but also by contact‐cementation, resulting in relatively large moduli for a given porosity, and by admixtures of clay and fine silica, which results in relatively small moduli for a given porosity. Based on a concept of solids suspended in pore fluids as well as composing the rock frame, we model P‐wave and S‐wave moduli of dry and wet plug samples by an effective‐medium Hashin–Shtrikman model, using chemical, mineralogical and textural input. For a given porosity, the elastic moduli correspond to a part of the solid (the iso‐frame value) forming the frame of an Upper Hashin–Shtrikman bound, whereas the remaining solid is modelled as suspended in the pore fluid. The iso‐frame model is thus a measure of the pore‐stiffness or degree of cementation of the chalk. The textural and mineralogical data may be assessed from logging data on spectral gamma radiation, density, sonic velocity and water saturation in a hydrocarbon zone, whereas the iso‐frame value of a chalk may be assessed from the density and acoustic P‐wave logs alone. The iso‐frame concept may thus be directly used in conventional log‐analysis and is a way of incorporating sonic‐logging data. The Rigs‐1 and Rigs‐2 wells in the South Arne field penetrate the chalk at the same depth but differ in porosity and in water saturation although almost the entire chalk interval has irreducible water saturation. Our model, combined with petrographic data, indicates that the difference in porosity is caused by a higher degree of pore‐filling cementation in Rigs‐1. Petrographic data indicate that the difference in water saturation is caused by a higher content of smectite in the pores of Rigs‐1. In both wells, we find submicron‐size diagenetic quartz.     

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.     

Acoustic and petrophysical relationships in low-shale sandstone reservoir rocks

This paper describes the measurements of the acoustic and petrophysical properties of two suites of low‐shale sandstone samples from North Sea hydrocarbon reservoirs, under simulated reservoir conditions. The acoustic velocities and quality factors of the samples, saturated with different pore fluids (brine, dead oil and kerosene), were measured at a frequency of about 0.8 MHz and over a range of pressures from 5 MPa to 40 MPa. The compressional‐wave velocity is strongly correlated with the shear‐wave velocity in this suite of rocks. The ratio V_P/V_S varies significantly with change of both pore‐fluid type and differential pressure, confirming the usefulness of this parameter for seismic monitoring of producing reservoirs. The results of quality factor measurements were compared with predictions from Biot‐flow and squirt‐flow loss mechanisms. The results suggested that the dominating loss in these samples is due to squirt‐flow of fluid between the pores of various geometries. The contribution of the Biot‐flow loss mechanism to the total loss is negligible. The compressional‐wave quality factor was shown to be inversely correlated with rock permeability, suggesting the possibility of using attenuation as a permeability indicator tool in low‐shale, high‐porosity sandstone reservoirs.     

Effect of pore geometry on Gassmann fluid substitution

Although there is no assumption of pore geometry in derivation of Gassmann's equation, the pore geometry is in close relation with hygroscopic water content and pore fluid communication between the micropores and the macropores. The hygroscopic water content in common reservoir rocks is small, and its effect on elastic properties is ignored in the Gassmann theory. However, the volume of hygroscopic water can be significant in shaly rocks or rocks made of fine particles; therefore, its effect on the elastic properties may be important. If the pore fluids in microspores cannot reach pressure equilibrium with the macropore system, assumption of the Gassmann theory is violated. Therefore, due to pore structure complexity, there may be a significant part of the pore fluids that do not satisfy the assumption of the Gassmann theory. We recommend that this part of pore fluids be accounted for within the solid rock frame and effective porosity be used in Gassmann's equation for fluid substitution. Integrated study of ultrasonic laboratory measurement data, petrographic data, mercury injection capillary pressure data, and nuclear magnetic resonance T₂ data confirms rationality of using effective porosity for Gassmann fluid substitution. The effective porosity for Gassmann's equation should be frequency dependent. Knowing the pore geometry, if an empirical correlation between frequency and the threshold pore‐throat radius or nuclear magnetic resonance T₂ could be set up, Gassmann's equation can be applicable to data measured at different frequencies. Without information of the pore geometry, the irreducible water saturation can be used to estimate the effective porosity.     

Borehole-guided AVO analysis of P-P and P-S reflections: Quantifying uncertainty on density estimates

Seismic properties of isotropic elastic formations are characterized by the three parameters: acoustic impedance, Poisson's ratio and density. Whilst the first two are usually well estimated by analysing the amplitude variation with angle (AVA) of reflected P‐P waves, density is known to be poorly resolved. However, density estimates would be useful in many situations encountered in oil and gas exploration, in particular, for minimizing risks in looking ahead while drilling. We design a borehole seismic experiment to investigate the reliability of AVA extracted density. Receivers are located downhole near the targeted reflectors and record reflected P‐P and converted P‐S waves. A non‐linear, wide‐angle‐based Bayesian inversion is then used to access the a posteriori probability distributions associated with the estimation of the three isotropic elastic parameters. The analysis of these distributions suggests that the angular variation of reflected P‐S amplitudes provides additional substantial information for estimating density, thus reducing the estimate uncertainty variance by more than one order of magnitude, compared to using only reflected P‐waves.     

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.     

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.     

Velocity–porosity relationships: Predictive velocity model for cemented sands composed of multiple mineral phases

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.     

复杂孔隙储层三维岩石物理模版

复杂孔隙储层往往同时发育孔缝洞等多种孔隙类型,这种孔隙结构的复杂性使得岩石的速度与孔隙度之间的相关性很差.经典的二维岩石物理模版只研究弹性参数与孔隙度和饱和度之间的定量关系,而不考虑孔隙结构的影响,用这样的模版来预测复杂孔隙储层的物性参数时带来很大偏差.本文首先证明多重孔隙岩石的干骨架弹性参数可以用一个等效孔隙纵横比的单重孔隙岩石物理模型来模拟;进而基于等效介质岩石物理理论和Gassmann方程,建立一个全新的三维岩石物理模版,用它来建立复杂孔隙岩石的弹性性质与孔隙扁度及孔隙度和饱和度之间的定量关系;在此基础上,预测复杂储层的孔隙扁度、孔隙度以及孔隙中所包含的流体饱和度.实际测井和地震反演数据试验表明,三维岩石物理模版可有效提高复杂孔隙储层参数的预测精度.     

Explicit use of the Biot coefficient in predicting shear-wave velocity of water-saturated sediments

Predicting the shear‐wave (S‐wave) velocity is important in seismic modelling, amplitude analysis with offset, and other exploration and engineering applications. Under the low‐frequency approximation, the classical Biot–Gassmann theory relates the Biot coefficient to the bulk modulus of water‐saturated sediments. If the Biot coefficient under in situ conditions can be estimated, the shear modulus or the S‐wave velocity can be calculated. The Biot coefficient derived from the compressional‐wave (P‐wave) velocity of water‐saturated sediments often differs from and is less than that estimated from the S‐wave velocity, owing to the interactions between the pore fluid and the grain contacts. By correcting the Biot coefficients derived from P‐wave velocities of water‐saturated sediments measured at various differential pressures, an accurate method of predicting S‐wave velocities is proposed. Numerical results indicate that the predicted S‐wave velocities for consolidated and unconsolidated sediments agree well with measured velocities.     

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.     

连续胶结声速理论胶结半径表达式的一般性推广及应用

针对Dvorkin 和Nur （1996） 提出的连续胶结声速理论（CCT）中的胶结半径表达式仅适用于孔隙式胶结疏松砂岩的局限性,通过胶结物与颗粒之间的空间几何关系,在胶结物中心厚度不为零的前提下,推导了胶结物胶结半径的一般表达式,并考察了胶结物中心厚度对疏松砂岩声波速度的影响,探讨了该表达式在基底式胶结疏松砂岩纵横波速度预测中的应用.结果表明：随胶结物中心厚度变大,纵、横波速度均减小,且孔隙度越大,胶结物含量越少,速度下降越快;孔隙度或胶结物含量不变时,纵横波速比随胶结物中心厚度的增大而增大;纵横波速比随孔隙度的变化规律与胶结物中心厚度有关,当胶结物中心厚度较小时,孔隙度增大,纵横波速比略微减小,而当胶结物中心厚度较大时,孔隙度的增大会引起纵横波速比略微增大;对于基底式胶结疏松砂岩,使用推广后表达式修正的CCT模型相对原CCT模型能够更好地预测其声波速度,同时发现,利用其纵横波速比无法预测由孔隙度或胶结物含量变化引起的疏松砂岩软硬的变化,但是在胶结物含量或孔隙度不变的情况下,纵横波速比可指示由胶结物中心厚度变化引起的疏松砂岩软硬的变化.     

Nonlinear simultaneous inversion of pore structure and physical parameters based on elastic impedance

Carbonate reservoirs have complex pore structures, which not only significantly affect the elastic properties and seismic responses of the reservoirs but also affect the accuracy of the prediction of the physical parameters. The existing rockphysics inversion methods are mainly designed for clastic rocks, and the inversion objects are generally porosity and water saturation. The data used are primarily based on the elastic parameters, and the inversion methods are mainly linear approximations. To date, there has been a lack of a simultaneous pore structure and physical parameter inversion method for carbonate reservoirs. To solve these problems, a new Bayesian nonlinear simultaneous inversion method based on elastic impedance is proposed. This method integrates the differential effective medium model of multiple-porosity rocks, Gassmann equation,Amplitude Versus Offset(AVO) theory, Bayesian theory, and a nonlinear inversion algorithm to achieve the simultaneous quantitative prediction of the pore structure and physical parameters of complex porous reservoirs. The forward modeling indicates that the contribution of the pore structure, i.e., the pore aspect ratio, to the AVO response and elastic impedance is second only to that of porosity and is far greater than that of water saturation. The application to real data shows that the new inversion method for determining the pore structure and physical parameters directly from pre-stack data can accurately predict a reservoir's porosity and water saturation and can evaluate the pore structure of the effective reservoir.     

Analytical approximations of bulk and shear moduli for dry rock based on the differential effective medium theory

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.     

Elastic properties of double-porosity rocks using the differential effective medium model

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.     

A triple porosity scheme for fluid/solid substitution: theory and experiment

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.     

模拟天然气水合物的岩石物理特性模型实验

针对水合物沉积的悬浮、颗粒接触和胶结三种微观模式,制作一组微弱胶结非固结高孔隙度人造样品和颗粒填充渐变的三维物理模型. 通过物理模型实验研究天然气水合物物性参数的敏感性. 实验结果表明：在弱颗粒间胶结物和低有效应力的固结差的沉积物中,声波对孔隙流体性质较敏感. 随着温度的降低颗粒胶结,改变原有沉积物的岩石物理特性,速度、弹性模量和频率升高,声波衰减和Vp/VS减小,沉积层内的反射波消隐.     

Influence of subsurface injection on time‐lapse seismic: laboratory studies at seismic and ultrasonic frequencies

Seismic monitoring of reservoir and overburden performance during subsurface CO₂ storage plays a key role in ensuring efficiency and safety. Proper interpretation of monitoring data requires knowledge about the rock physical phenomena occurring in the subsurface formations. This work focuses on rock stiffness and elastic velocity changes of a shale overburden formation caused by both reservoir inflation induced stress changes and leakage of CO₂ into the overburden. In laboratory experiments, Pierre shale I core plugs were loaded along the stress path representative for the in situ stress changes experienced by caprock during reservoir inflation. Tests were carried out in a triaxial compaction cell combining three measurement techniques and permitting for determination of (i) ultrasonic velocities, (ii) quasistatic rock deformations, and (iii) dynamic elastic stiffness at seismic frequencies within a single test, which allowed to quantify effects of seismic dispersion. In addition, fluid substitution effects connected with possible CO₂ leakage into the caprock formation were modelled by the modified anisotropic Gassmann model. Results of this work indicate that (i) stress sensitivity of Pierre shale I is frequency dependent; (ii) reservoir inflation leads to the increase of the overburden Young's modulus and Poisson's ratio; (iii) in situ stress changes mostly affect the P‐wave velocities; (iv) small leakage of the CO₂ into the overburden may lead to the velocity changes, which are comparable with one associated with geomechanical influence; (v) non‐elastic effects increase stress sensitivity of an acoustic waves; (iv) and both geomechanical and fluid substitution effects would create significant time shifts, which should be detectable by time‐lapse seismic.     

Prestack amplitude versus angle inversion for Young's modulus and Poisson's ratio based on the exact Zoeppritz equations

Elastic parameters such as Young's modulus, Poisson's ratio, and density are very important characteristic parameters that are required to properly characterise shale gas reservoir rock brittleness, evaluate gas characteristics of reservoirs, and directly interpret lithology and oil‐bearing properties. Therefore, it is significant to obtain accurate information of these elastic parameters. Conventionally, they are indirectly calculated by the rock physics method or estimated by approximate formula inversion. The cumulative errors caused by the indirect calculation and low calculation accuracy of the approximate Zoeppritz equations make accurate estimation of Young's modulus, Poisson's ratio, and density difficult in the conventional method. In this paper, based on the assumption of isotropy, we perform several substitutions to convert the Zoeppritz equations from the classical form to a new form containing the chosen elastic constants of Young's modulus, Poisson's ratio, and density. The inversion objective function is then constructed by utilising Bayesian theory. Meanwhile, the Cauchy distribution is introduced as a priori information. We then combine the idea of generalised linear inversion with an iterative reweighed least squares algorithm in order to solve the problem. Finally, we obtain the iterative updating formula of the three elastic parameters and achieve the direct inversion of these elastic parameters based on the exact Zoeppritz equations. Both synthetic and field data examples show that the new method is not only able to obtain the two elastic parameters of Young's modulus and Poisson's ratio stably and reasonably from prestack seismic data but also able to provide an accurate estimation of density information, which demonstrates the feasibility and effectiveness of the proposed method. The proposed method offers an efficient seismic method to identify a “sweet spot” within a shale gas reservoir.     

煤层气储层含气量与其弹性参数之间的关系——思考与初探

首先研究了天然气AVO技术的岩石物理基础--Gassmann方程和Biot理论(以下统称为"Gassmann-Biot理论")--对煤层气AVO技术的适用性.根据该理论创始人在建立其理论时的假设条件、煤层气储层的双相孔隙特征、煤层气的双相赋存特征,本文推理认为,由于煤层气储层的基质型孔隙体系的连通性差,裂隙性孔隙在宏观上是非均质的,并且是各向异性的,因此,总体上来说,Gassmann-Biot理论不完全适用于煤层气储层.特别地,当煤层的水饱和状态保持不变而煤层的含气量变化时,因为煤层中孔(裂)隙中流体的体积压缩模量不变或基本不变,即使煤层的弹性参数发生变化,Gassmann-Biot理论也不可能预测其变化趋势.因此,天然气AVO技术的岩石物理基础完全地不适用于水饱和煤层气储层.研究发现,煤层气储层含气量与其密度、纵波速度、横波速度之间存在负相关关系,即含气量高,密度小、纵波速度小、横波速度小;含气量低,密度大、纵波速度大、横波速度大.但是,这些负相关关系不是现有岩石物理理论能够预测或能够解释的.依据煤层气地质学理论以及负相关关系与现有岩石物理理论的一致性,本文提供了对某勘探区A号煤层含气量与其密度、纵波速度、横波速度之间负相关关系的解释,并认为煤层气储层的含气量与其弹性参数之间的负相关关系可能是这类储层内在的固有的规律性的关系.本文证明含气量与其密度、纵波速度、横波速度之间负相关关系可以作为煤层气AVO技术的岩石物理基础,建立了AVO异常与煤层气储层"甜点(即富集高渗部位)"之间的关系,从而能够使用AVO异常探测煤层气富集高渗部位.