基于方位各向异性弹性阻抗的裂缝岩石物理参数反演方法研究

裂缝储层岩石物理参数的准确获得对地下裂缝预测具有重要意义,而叠前地震反演是获得裂缝岩石物理参数的有效手段.本文从裂缝岩石物理等效模型的构建出发,从测井数据上估测了裂缝岩石物理参数,通过推导含裂缝岩石物理参数的方位各向异性弹性阻抗公式,探讨了基于方位各向异性弹性阻抗的裂缝岩石物理参数地震反演方法.实际工区地震数据应用表明,基于方位各向异性弹性阻抗的裂缝岩石物理参数反演方法合理、可靠,可以降低裂缝岩石物理参数估测的不确定性,为地下裂缝预测提供有力的依据.     

Azimuthally pre-stack seismic inversion for orthorhombic anisotropy driven by rock physics

Based on the long-wavelength approximation, a set of parallel vertical fractures embedded in periodic thin interbeds can be regarded as an equivalent orthorhombic medium. Rock physics is the basis for constructing the relationship between fracture parameters and seismic response. Seismic scattering is an effective way to inverse anisotropic parameters. In this study, we propose a reliable method for predicting the Thomsen’s weak anisotropic parameters and fracture weaknesses in an orthorhombic fractured reservoir using azimuthal pre-stack seismic data. First, considering the influence of fluid substitution in mineral matrix, porosity, fractures and anisotropic rocks, we estimate the orthorhombic anisotropic stiffness coefficients by constructing an equivalent rock physics model for fractured rocks. Further, we predict the logging elastic parameters, Thomsen’s weak parameters, and fracture weaknesses to provide the initial model constraints for the seismic inversion. Then, we derive the P-wave reflection coefficient equation for the inversion of Thomsen’s weak anisotropic parameters and fracture weaknesses. Cauchy-sparse and smoothing-model constraint regularization taken into account in a Bayesian framework, we finally develop a method of amplitude variation with angles of incidence and azimuth (AVAZ) inversion for Thomsen’s weak anisotropic parameters and fracture weaknesses, and the model parameters are estimated by using the nonlinear iteratively reweighted least squares (IRLS) strategy. Both synthetic and real examples show that the method can directly estimate the orthorhombic characteristic parameters from the azimuthally pre-stack seismic data, which provides a reliable seismic inversion method for predicting Thomsen’s weak anisotropic parameters and fracture weaknesses.     

基于贝叶斯线性AVAZ的TTI介质裂缝参数反演

裂缝储层岩石物理参数的准确获得对地下裂缝预测具有重要意义,而叠前方位AVA地震反演是获得裂缝岩石物理参数的有效手段.假设地下岩石为倾斜横向各向同性（TTI）介质,本文从裂缝岩石物理等效模型的构建出发,从测井数据中估计出纵横波相对反射系数和裂缝柔度参数.通过推导含裂缝柔度的方位各向异性反射系数公式,基于贝叶斯反演框架建立了P波线性AVAZ反演方法.合成地震数据应用表明基于贝叶斯理论的TTI介质裂缝柔度反演方法具有一定抗噪性,可以降低裂缝柔度估测的不确定性,为地下裂缝预测提供有力的依据.     

Reconstruction of the layer anisotropic elastic parameters and high-resolution fracture characterization from P-wave data: a case study using seismic inversion and Bayesian rock physics parameter estimation

Wide-azimuth seismic data can be used to derive anisotropic parameters on the subsurface by observing variation in subsurface seismic response along different azimuths. Layer-based high-resolution estimates of components of the subsurface anisotropic elastic tensor can be reconstructed by using wide-azimuth P-wave data by combining the kinematic information derived from anisotropic velocity analysis with dynamic information obtained from amplitude versus angle and azimuth analysis of wide-azimuth seismic data. Interval P-impedance, S-impedance and anisotropic parameters associated with anisotropic fracture media are being reconstructed using linearized analysis assuming horizontal transverse anisotropy symmetry. In this paper it is shown how additional assumptions, such as the rock model, can be used to reduce the degrees of freedom in the estimation problem and recover all five anisotropic parameters. Because the use of a rock model is needed, the derived elastic parameters are consistent with the rock model and are used to infer fractured rock properties using stochastic rock physics inversion. The inversion is based on stochastic rock physics modelling and maximum a posteriori estimate of both porosity and crack density parameters associated with the observed elastic parameters derived from both velocity and amplitude versus angle and azimuth analysis. While the focus of this study is on the use of P-wave reflection data, we also show how additional information such as shear wave splitting and/or anisotropic well log data can reduce the assumptions needed to derive elastic parameter and rock properties.     

Seismic characterization of reservoirs with multiple fracture sets using velocity and attenuation anisotropy data

Knowledge about the spatial distribution of the fracture density and the azimuthal fracture orientation can greatly help in optimizing production from fractured reservoirs. Frequency-dependent seismic velocity and attenuation anisotropy data contain information about the fractures present in the reservoir. In this study, we use the measurements of velocity and attenuation anisotropy data corresponding to different seismic frequencies and azimuths to infer information about the multiple fracture sets present in the reservoir. We consider a reservoir model with two sets of vertical fractures characterized by unknown azimuthal fracture orientations and fracture densities. Frequency-dependent seismic velocity and attenuation anisotropy data is computed using the effective viscoelastic stiffness tensor and solving the Christoffel equation. A Bayesian inversion method is then applied to measurements of velocity and attenuation anisotropy data corresponding to different seismic frequencies and azimuth to estimate the azimuthal fracture orientations and the fracture densities, as well as their uncertainties. Our numerical examples suggest that velocity anisotropy data alone cannot recover the unknown fracture parameters. However, an improved estimation of the unknown fracture parameters can be obtained by joint inversion of velocity and attenuation anisotropy data.     

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.     

岩石物理驱动的储层裂缝参数与物性参数概率地震反演方法

长波长假设条件下,各向同性背景地层中发育一组平行排列的垂直裂缝可等效为具有水平对称轴的横向各向同性（HTI）介质.基于不同观测方位的岩石地震响应特征变化,宽方位地震数据不仅可实现裂缝岩石弹性参数与各向异性参数的预测,同时也蕴含着丰富的孔隙度等储层物性参数信息.本文结合实际地震资料提出了贝叶斯框架下岩石物理驱动的储层裂缝参数与物性参数概率地震联合反演方法,首先基于AVAZ反演裂缝岩石的弹性参数与各向异性参数,并在此基础上通过统计岩石物理模型表征孔隙度、裂缝密度等各向异性介质储层参数与裂缝岩石参数的相互关联,并采用马尔科夫链蒙特卡洛（MCMC）抽样方法进行大量样本的随机模拟,使用期望最大化（EM）算法估计后验条件概率分布,最终寻找最大后验条件概率对应的孔隙度、裂缝密度等HTI裂缝介质储层参数即为反演结果.测井及实际地震数据处理表明,该方法能够稳定合理地从方位地震资料中获取裂缝岩石弹性参数与各向异性参数,并提供了一种较为可靠的孔隙度、裂缝密度等裂缝介质储层参数概率地震反演方法.     

Characterization of fractured reservoirs using a consistent stiffness‐permeability model: focus on the effects of fracture aperture

In this paper we propose a method for the characterization of naturally fractured reservoirs by quantitative integration of seismic and production data. The method is based on a consistent theoretical frame work to model both effective hydraulic and elastic properties of fractured porous media and a (non‐linear) Bayesian method of inversion that provides information about uncertainties as well as mean (or maximum likelihood) values. We model a fractured reservoir as a porous medium containing a single set of vertical fractures characterized by an unknown fracture density, azimuthal orientation and aperture. We then look at the problem of fracture parameter estimation as a non‐linear inverse problem and try to estimate the unknown fracture parameters by joint inversion of seismic amplitude versus angle and azimuth data and dynamic production data. Once the fracture parameters have been estimated the corresponding effective stiffness and permeability tensors can be estimated using consistent models. A synthetic example is provided to clearly explain and test the workflow. It shows that seismic and production data complement each other, in the sense that the seismic data resolve a non‐uniqueness in the fracture orientation and the production data help to recover the true fracture aperture and permeability, because production data are more sensitive to the fracture aperture than the seismic data.     

Rock physics modeling of heterogeneous carbonatereservoirs： porosity estimation and hydrocarbon detection

In heterogeneous natural gas reservoirs, gas is generally present as small patch-like pockets embedded in the water-saturated host matrix. This type of heterogeneity, alsocalled ＂patchy saturation＂, causes significant seismic velocity dispersion and attenuation. Toestablish the relation between seismic response and type of fluids, we designed a rock physicsmodel for carbonates. First, we performed CT scanning and analysis of the fluid distributionin the partially saturated rocks. Then, we predicted the quantitative relation between the waveresponse at different frequency ranges and the basic lithological properties and pore fluids.A rock physics template was constructed based on thin section analysis of pore structuresand seismic inversion. This approach was applied to the limestone gas reservoirs of the rightbank block of the Amu Darya River. Based on poststack wave impedance and prestack elasticparameter inversions, the seismic data were used to estimate rock porosity and gas saturation.The model results were in ~ood a~reement with the production regime of the wells.     

叠前反演和地震吸收技术在复杂天然气藏地震预测中的应用

针对某复杂断块天然气目标储层,在岩石物理分析的指导下,综合利用地质、地震、测井等资料,提出了一套面向复杂天然气藏的叠前地震预测技术.首先基于地震岩石物理分析得到的初始横波信息,采用叠前贝叶斯非线性三参数反演得到了井旁控制点处精确纵横波速度和密度信息,然后通过叠前/叠后联合反演技术实现了面向目标的弹性阻抗体反演及含气储层敏感参数直接提取,最后结合小波变换时频谱分析的方法从叠前地震资料中估算地层吸收参数值,提高天然气藏识别精度.实际应用表明,综合各种叠前地震预测技术,可以大大提高对复杂天然气藏的识别精度,降低勘探风险.     

Integrating basin modeling with seismic technology and rock physics

We explore the link between basin modelling and seismic inversion by applying different rock physics models. This study uses the E‐Dragon II data in the Gulf of Mexico. To investigate the impact of different rock physics models on the link between basin modelling and seismic inversion, we first model relationships between seismic velocities and both (1) porosity and (2) effective stress for well‐log data using published rock physics models. Then, we build 1D basin models to predict seismic velocities derived from basin modelling with different rock physics models, in a comparison with average sonic velocities measured in the wells. Finally, we examine how basin modelling outputs can be used to aid seismic inversion by providing constraints for the background low‐frequency model. For this, we run different scenarios of inverting near angle partial stack seismic data into elastic impedances to test the impact of the background model on the quality of the inversion results. The results of the study suggest that the link between basin modelling and seismic technology is a two‐way interaction in terms of potential applications, and the key to refine it is establishing a rock physics models that properly describes changes in seismic signatures reflecting changes in rock properties.     

基于贝叶斯框架的各向异性页岩储层岩石物理反演技术

页岩岩石物理建模旨在建立页岩矿物组分、微观结构、流体填充与岩石弹性参数的关系.对四川盆地龙马溪组页岩进行岩石物理建模研究,针对页岩黏土含量高、层间微裂缝发育等特点,利用Backus平均理论描述页岩黏土矿物弹性参数,利用Chapman理论计算与水平微裂缝有关的VTI各向异性,并利用Bond变换考虑地层倾角的影响.提出以黏土矿物纵、横波速度和孔隙纵横比为拟合参数进行岩石物理反演的方法,并引入贝叶斯框架减小反演的多解性.由已知的黏土矿物纵、横波速度和孔隙纵横比作为先验信息,并以测井纵、横波速度作为约束条件建立反演的目标函数,同时利用粒子群算法进行最优化搜索.计算结果表明,基于先验约束和粒子群算法的反演方法能够较准确地反演黏土矿物的弹性参数、孔隙形态参数以及裂缝密度等参数.计算得到的黏土纵、横波速度较高,并且在一定范围内变化,这可能与龙马溪组页岩的黏土矿物组分中具有较高弹性模量的伊利石含量较高有关,同时也与黏土定向排列等微观物性特征有关.反演得到的裂缝密度与纵波各向异性参数ε呈明显的正相关,而与横波各向异性参数γ相关性较小.另外,页岩各向异性参数与黏土垂向的纵横波速度有较强的相关性.     

基于弹性阻抗的储层物性参数预测方法

储层物性参数是储层描述的重要参数,常规的基于贝叶斯理论的储层物性参数反演方法大多是通过反演获得的弹性参数进一步转换而获得物性参数,本文提出一种基于弹性阻抗数据预测储层物性参数的反演方法.该方法主要通过建立可以表征弹性阻抗与储层物性参数之间关系的统计岩石物理模型,联合蒙特卡罗仿真模拟技术,在贝叶斯理论框架的指导下,应用期望最大化算法估计物性参数的后验概率分布,最终实现储层物性参数反演.经过模型测试和实际资料的处理,其结果表明本文提出的方法具有预测精度高,稳定性强,横向连续性好等优点.     

基于碳酸盐岩裂缝岩石物理模型的横波速度和各向异性参数预测

高角度缝隙充填的碳酸盐岩储层可以等效为具有水平对称轴的横向各向同性介质.本文提出了适用于裂缝型碳酸盐岩的岩石物理模型构建流程,重点介绍了在碳酸盐岩各向同性背景中,综合利用微小裂隙模型和线性滑动模型添加缝隙系统,并分析了当缝隙充填不同流体时,各向异性参数随纵横波速比的变化特征.同时本文讨论了裂缝密度和缝隙充填流体对地震反射系数的影响,推导了不同类型流体充填时储层反射系数与裂缝密度的近似关系式,阐述了各向异性流体替换理论,最终实现饱含流体碳酸盐岩裂缝储层的纵横波速度和各向异性参数的估测.选取某碳酸盐岩工区A井对该方法进行试算,结果表明基于碳酸盐岩裂缝岩石物理模型估算的纵横波速度值与测井值吻合较好,而且估测所得的各向异性参数值也能够较好地反映出裂缝储层位置.     

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.     

致密砂岩气藏裂隙-孔隙型弹性岩石物理模板研究:以川西坳陷A区为例

相对于常规砂岩,致密砂岩在岩石物理性质、力学性质等方面具有明显差异,并呈现出很强的非均质性.岩石物理模型能将储层参数与地震特性信息联系起来,因此可以作为致密砂岩储层参数与地震特性信息转换的桥梁.常规的岩石物理模型通常只考虑单一因素(例如非均匀性,单一孔隙,单一尺度等),建立的岩石物理模板并不适用于致密砂岩.本文针对高饱和气、微裂隙发育、非均质性强的致密砂岩储层,利用Voigt-Reuss-Hill模型计算混合矿物的弹性模量,采用微分等效介质(DEM)模型描述含裂隙、孔隙岩石的骨架弹性模量,基于Biot-Rayleigh波动方程构建了岩石物理弹性模板,给出了致密砂岩储层弹性参数与物性的关系.基于测井数据和实验数据对岩石物理弹性模板进行校正,并将校正后的岩石物理弹性模板结合叠前地震资料应用于川西地区储层孔隙度与裂隙含量预测.结果显示,反演裂隙含量、孔隙度与储层试气报告、测井孔隙度基本吻合,表明该模板能够较合理地应用于致密砂岩储层孔隙度及裂隙含量解释中.     

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.     

CO2 saturation estimates at Sleipner (North Sea) from seismic tomography and rock physics inversion

CO₂ saturations are estimated at Sleipner using a two-step imaging workflow. The workflow combines seismic tomography (full-waveform inversion) and rock physics inversion and is applied to a two-dimensional seismic line located near the injection point at Sleipner. We use baseline data (1994 vintage, before CO₂ injection) and monitor data that was acquired after 12 years of CO₂ injection (2008 vintage). P-wave velocity models are generated using the Full waveform inversion technology and then, we invert selected rock physics parameters using an rock physics inversion methodology. Full waveform inversion provides high-resolution P-wave velocity models both for baseline and monitor data. The physical relations between rock physics properties and acoustic wave velocities in the Utsira unconsolidated sandstone (reservoir formation) are defined using a dynamic rock physics model based on well-known Biot–Gassmann theories. For data prior to injection, rock frame properties (porosity, bulk and shear dry moduli) are estimated using rock physics inversion that allows deriving physically consistent properties with related uncertainty. We show that the uncertainty related to limited input data (only P-wave velocity) is not an issue because the mean values of parameters are correct. These rock frame properties are then used as a priori constraint in the monitor case. For monitor data, the Full waveform inversion results show nicely resolved thin layers of CO₂–brine saturated sandstones under intra-reservoir shale layers. The CO₂ saturation estimation is carried out by plugging an effective fluid phase in the rock physics model. Calculating the effective fluid bulk modulus of the brine–CO₂ mixture (using Brie equation in our study) is shown to be the key factor to link P-wave velocity to CO₂ saturation. The inversion tests are done with several values of Brie/patchiness exponent and show that the CO₂ saturation estimates are varying between 0.30 and 0.90 depending on the rock physics model and the location in the reservoir. The uncertainty in CO₂ saturation estimation is usually lower than 0.20. When the patchiness exponent is considered as unknown, the inversion is less constrained and we end up with values of exponent varying between 5 and 20 and up to 33 in specific reservoir areas. These estimations tend to show that the CO₂–brine mixing is between uniform and patchy mixing and variable throughout the reservoir.     

Bayesian seismic inversion for estimating fluid content and fracture parameters in a gas-saturated fractured porous reservoir

Understanding the effects of in situ fluid content and fracture parameters on seismic characteristics is important for the subsurface exploration and production of fractured porous rocks. The ratio of normal-to-shear fracture compliance is typically utilized as a fluid indicator to evaluate anisotropy and identify fluids filling the fractures, but it represents an underdetermined problem because this fluid indicator varies as a function of both fracture geometry and fluid content. On the bases of anisotropic Gassmann's equation and linear-slip model, we suggest an anisotropic poroelasticity model for fractured porous reservoirs. By combining a perturbed stiffness matrix and asymptotic ray theory, we then construct a direct relationship between the PP-wave reflection coefficients and characteristic parameters of fluids(P-and S-wave moduli) and fractures(fracture quasi-weaknesses), thereby decoupling the effects of fluid and fracture properties on seismic reflection characterization.By incorporating fracture quasi-weakness parameters, we propose a novel parameterization method for elastic impedance variation with offset and azimuth(EIVOA). By incorporating wide-azimuth observable seismic reflection data with regularization constraints, we utilize Bayesian seismic inversion to estimate the fluid content and fracture parameters of fractured porous rocks. Tests on synthetic and real data demonstrate that fluid and fracture properties can be reasonably estimated directly from azimuthal seismic data and the proposed approach provides a reliable method for fluid identification and fracture characterization in a gas-saturated fractured porous reservoir.     

非均匀正交各向异性特征参数地震散射反演方法研究

在长波长假设条件下,水平层状地层中发育一组垂直排列的裂缝构成了等效正交各向异性介质.各向异性参数与裂缝弱度参数的估算有助于非均匀各向异性介质的各向异性特征描述,而弹性逆散射理论是非均匀介质参数反演的有效途径.基于地震散射理论,我们首先推导了非均匀正交介质中纵波散射系数方程,并通过引入正交各向异性特征参数,提出了一种新颖的正交各向异性方位弹性阻抗参数化方法.为了提高反演的稳定性与横向连续性,我们发展了贝叶斯框架下的正交各向异性方位弹性阻抗反演方法,同时考虑了柯西稀疏约束正则化和平滑模型约束正则化,最终使用非线性的迭代重加权最小二乘策略实现了各向异性特征参数的稳定估算.模型和实际资料处理表明,反演结果与测井解释数据相吻合,证明了该方法能够稳定可靠地从方位叠前地震资料中获取各向异性特征参数,减小参数估算的不确定性,为非均匀正交介质的各向异性预测提供了一种高可靠性的地震反演方法.