A new energy density calculation method for reservoir delineation using seismic low-frequency signal

In comparison to high-frequency signals, low-frequency seismic signals suffer less from scattering and intrinsic attenuation during wave propagation, penetrate deeper strata and thus can provide more energy information related to the hydrocarbon reservoirs. Based on the asymptotic representation for the frequency-dependent reflections in the fluid-saturated pore-elastic media, we first derive a novel equation of the reservoir energy density and present an efficient workflow to calculate the reservoir energy density using low-frequency seismic data. Then, within a low-frequency range (from 1 to 30 Hz), we construct an objective function to determine the optimal frequency, using the energy densities calculated from the post-stack seismic traces close to the wells. Next, we can calculate the reservoir energy density using the instantaneous spectra of optimal frequency at the low-frequency end of the seismic spectrum. Tests on examples for synthetic and field data demonstrate that the proposed reservoir energy density can produce high-quality images for the fluid-saturated reservoirs, and it produces less background artefacts caused by elastic layers. This method provides a new way to detect the location of hydrocarbon reservoirs and characterize their spatial distribution.     

Seismic attenuation in porous rocks with random patchy saturation

Saturation of porous rocks with a mixture of two fluids has a substantial effect on seismic‐wave propagation. In particular, partial saturation causes significant attenuation and dispersion of the propagating waves due to the mechanism of wave‐induced fluid‐flow. Such flow arises when a passing wave induces different fluid pressures in regions of rock saturated by different fluids. Most models of attenuation and dispersion due to mesoscopic heterogeneities imply that fluid heterogeneities are distributed in a regular way. However, recent experimental studies show that mesoscopic heterogeneities have less idealized distributions and that the distribution itself affects attenuation and dispersion. Based on an approximation for the coherent wavefield in random porous media, we develop a model which assumes a continuous distribution of fluid heterogeneities. As this continuous random media approach assumes that there will be a distribution of different patch sizes, it is expected to be better suited to modelling experimental data. We also show how to relate the random functions to experimentally measurable parameters.     

Interaction of multiple courses of wave‐induced fluid flow in layered porous media

Different theoretical and laboratory studies on the propagation of elastic waves in layered hydrocarbon reservoir have shown characteristic velocity dispersion and attenuation of seismic waves. The wave‐induced fluid flow between mesoscopic‐scale heterogeneities (larger than the pore size but smaller than the predominant wavelengths) is the most important cause of attenuation for frequencies below 1 kHz. Most studies on mesoscopic wave‐induced fluid flow in the seismic frequency band are based on the representative elementary volume, which does not consider interaction of fluid flow due to the symmetrical structure of representative elementary volume. However, in strongly heterogeneous media with unsymmetrical structures, different courses of wave‐induced fluid flow may lead to the interaction of the fluid flux in the seismic band; this has not yet been explored. This paper analyses the interaction of different courses of wave‐induced fluid flow in layered porous media. We apply a one‐dimensional finite‐element numerical creep test based on Biot's theory of consolidation to obtain the fluid flux in the frequency domain. The characteristic frequency of the fluid flux and the strain rate tensor are introduced to characterise the interaction of different courses of fluid flux. We also compare the behaviours of characteristic frequencies and the strain rate tensor on two scales: the local scale and the global scale. It is shown that, at the local scale, the interaction between different courses of fluid flux is a dynamic process, and the weak fluid flux and corresponding characteristic frequencies contain detailed information about the interaction of the fluid flux. At the global scale, the averaged strain rate tensor can facilitate the identification of the interaction degree of the fluid flux for the porous medium with a random distribution of mesoscopic heterogeneities, and the characteristic frequency of the fluid flux is potentially related to that of the peak attenuation. The results are helpful for the prediction of the distribution of oil–gas patches based on the statistical properties of phase velocities and attenuation in layered porous media with random disorder.     

Low-frequency dilatational wave propagation through fully-saturated poroelastic media

The strong coupling of applied stress and pore fluid pressure, known as poroelasticity, is relevant to a number of applied problems arising in hydrogeology and reservoir engineering. The standard theory of poroelastic behavior in a homogeneous, isotropic, elastic porous medium saturated by a viscous, compressible fluid is due to Biot, who derived a pair of coupled partial differential equations that accurately predict the existence of two independent dilatational (compressional) wave motions, corresponding to in-phase and out-of-phase displacements of the solid and fluid phases, respectively. The Biot equations can be decoupled exactly after Fourier transformation to the frequency domain, but the resulting pair of Helmholtz equations cannot be converted to partial differential equations in the time domain and, therefore, closed-form analytical solutions of these equations in space and time variables cannot be obtained. In this paper we show that the decoupled Helmholtz equations can in fact be transformed to two independent partial differential equations in the time domain if the wave excitation frequency is very small as compared to a critical frequency equal to the kinematic viscosity of the pore fluid divided by the permeability of the porous medium. The partial differential equations found are a propagating wave equation and a dissipative wave equation, for which closed-form solutions are known under a variety of initial and boundary conditions. Numerical calculations indicate that the magnitude of the critical frequency for representative sedimentary materials containing either water or a nonaqueous phase liquid is in the kHz–MHz range, which is generally above the seismic band of frequencies. Therefore, the two partial differential equations obtained should be accurate for modeling elastic wave phenomena in fluid-saturated porous media under typical low-frequency conditions applicable to hydrogeological problems.     

Algorithms for staggered-grid computations for poroelastic,elastic, acoustic,and scalar wave equations

Heterogeneous wave equations are more complicated numerically than homogeneous wave equations, but are necessary for physical validity. A wide variety of numerical solutions of seismic wave equations is available, but most produce strong numerical artefacts and local instabilities where model parameters change rapidly. Accuracy and stability of heterogeneous equations is achieved through staggered-grid formulations. A new pseudospectral staggered-grid algorithm is developed for the poroelastic (Biot) equations. The algorithm may be reduced to handle the elastic and acoustic limits of the Biot equations. Comparisons of results from poroelastic, elastic, acoustic and scalar computations for a 2D model show that porous medium parameters may affect amplitudes significantly. The use of homogeneous wave equations for modelling of a heterogeneous medium, or of a centred rather than a staggered grid, or of simplified (e.g. acoustic) wave equations when elastic or poroelastic media are synthesized, may produce erroneous or ambiguous interpretations.     

基于数字岩心动态应力应变模拟的非均匀孔隙介质波致流固相对运动刻画

地震波传播激发的不同尺度的流固相对运动(宏观、中观和微观)是许多沉积岩地层中地震波频散和衰减的主要原因,然而野外观测和试验测量都难以对非均匀多孔介质孔隙压力弛豫物理过程进行精细刻画.通过数字岩石物理技术,本文建立了三个典型的数字岩心分别用于表征孔隙结构、岩石骨架和斑状饱和流体引起的非均质性,利用动态应力应变模拟技术计算数字岩心的位移和孔隙流体增量图像.通过分析和比较三个数字岩心的位移和孔隙压力增量图像,细致刻画了发生于非均匀含流体多孔介质内的宏观、中观和微观尺度的流固相对运动:1)宏观尺度的波致孔隙流体流动导致波长尺度上数字岩心不同区域的孔隙压力和位移差异;2)中观尺度的流体流动发生在软层与硬层之间、气层与液层之间;3)微观尺度的流体流动发生在孔隙内部或相邻孔隙之间.数值模拟试验也证明基于数字岩心的动态应力应变模拟技术可以从微观尺度上更好的理解波致孔隙流体流动发生的物理机理,从而为建立岩石骨架、孔隙流体、孔隙结构非均质性和弹性波频散-衰减特征的映射关系奠定基础.     

Seismic low-frequency-based calculation of reservoir fluid mobility and its applications

Low frequency content of seismic signals contains information related to the reservoir fluid mobility. Based on the asymptotic analysis theory of frequency-dependent reflectivity from a fluid-saturated poroelastic medium, we derive the computational implementation of reservoir fluid mobility and present the determination of optimal frequency in the implementation. We then calculate the reservoir fluid mobility using the optimal frequency instantaneous spectra at the low-frequency end of the seismic spectrum. The methodology is applied to synthetic seismic data from a permeable gas-bearing reservoir model and real land and marine seismic data. The results demonstrate that the fluid mobility shows excellent quality in imaging the gas reservoirs. It is feasible to detect the location and spatial distribution of gas reservoirs and reduce the non-uniqueness and uncertainty in fluid identification.     

Analysis of attenuation and dispersion of propagating wave due to the coexistence of three fluid phases in the pore volume

In exploration geophysics, the efforts to extract subsurface information from wave characteristics exceedingly depend on the construction of suitable rock physics model. Analysis of different rock physics models reveals that the strength and magnitude of attenuation and dispersion of propagating wave exceedingly depend on wave-induced fluid flow at multiple scales. In current work, a comprehensive analysis of wave attenuation and velocity dispersion is carried out at broad frequency range. Our methodology is based on Biot's poroelastic relations, by which variations in wave characteristics associated with wave-induced fluid flow due to the coexistence of three fluid phases in the pore volume is estimated. In contrast to the results of previous research, our results indicate the occurrence of two-time pore pressure relaxation phenomenon at the interface between fluids of disparate nature, that is, different bulk modulus, viscosity and density. Also, the obtained results are compatible with numerical results for the same 1D model which are accounted using Biot's poroelastic and quasi-static equation in frequency domain. Moreover, the effects of change in saturation of three-phase fluids were also computed which is the key task for geophysicist. The outcomes of our research reveal that pore pressure relaxation phenomenon significantly depends on the saturation of distinct fluids and the order of saturating fluids. It is also concluded that the change in the saturation of three-phase fluid significantly influences the characteristics of the seismic wave. The analysis of obtained results indicates that our proposed approach is a useful tool for quantification, identification and discrimination of different fluid phases. Moreover, our proposed approach improves the accuracy to predict dispersive behaviour of propagating wave at sub-seismic and seismic frequencies.     

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.     

Acoustic wave propagation in saturated porous media: reformulation of the Biot/Squirt flow theory

A model of wave propagation in fluid-saturated porous media is developed where the principal fluid/solid interaction mode affecting the propagation of the acoustic wave results from the conjunction of the Biot and the Squirt flow mechanism. The difference between the original Biot/Squirt (BISQ) flow theory and the new theory, which we call the reformulated BISQ, is that the average fluid pressure term appearing in the dynamic equation for a two component solid/fluid continuum is independent of squirt flow length. P-velocity and attenuation relate to measurable rock physical parameters: the Biot's poroelastic constants, porosity, permeability, pore fluid compressibility and viscosity. Modelling shows that velocity and attenuation dispersion obtained using the reformulated BISQ theory are of the same order of magnitude as those obtained using the original BISQ theory. Investigation on permeability effect on velocity and attenuation dispersion indicate that the transition zone in velocity and attenuation peak, occurring both at the relaxation frequency, shifts toward high frequency when permeability decreases. This behaviour agrees with Biot's theory prediction.     

基于自适应杂交遗传算法的CO_2地质封存的储层参数反演研究

二氧化碳地质封存是减少温室气体排放和减缓温室效应的重要手段.二氧化碳封存的一个重要组成部分是地震监测,即用地震的方法监测封存后的二氧化碳的分布变化.为了实现这个目标,需要建立储层参数与地震性质之间的关系(岩石物理模型)和从地震监测数据中反演获得储层流体的饱和度等参数.首先,本文以Biot理论为基础,结合多相流模型研究了多个物理参数(孔隙度、二氧化碳饱和度、温度和压力等)对同时含有二氧化碳和水的孔隙介质的波速和衰减等属性的影响.结果表明:孔隙度和二氧化碳饱和度对岩石的频散和衰减属性影响强烈,而温度和压力通过孔隙流体性质对岩石的波速产生影响.然后,本文基于含多相流的Biot理论,应用抗干扰能力强、且具有更好的局部搜索能力和抗早熟能力的自适应杂交遗传算法对实际数据进行了反演研究.对岩心实验数据的反演研究表明了算法的有效性,而且表明含多相流的Biot理论能够很好地解释水和二氧化碳饱和岩石的波速特征.最后,我们将自适应杂交遗传算法应用于实际封存项目的地震监测数据,获得了封存后不同时期的二氧化碳饱和度,达到了用地震方法监测二氧化碳分布的目的.     

When 4D seismic is not applicable: Alternative monitoring scenarios for the Arab-D reservoir in the Ghawar Field

Ghawar, the largest oilfield in the world, produces oil from the Upper Jurassic Arab‐D carbonate reservoir. The high rigidity of the limestone–dolomite reservoir rock matrix and the small contrast between the elastic properties of the pore fluids, i.e. oil and water, are responsible for the weak 4D seismic effect due to oil production. A feasibility study was recently completed to quantify the 4D seismic response of reservoir saturation changes as brine replaced oil. The study consisted of analysing reservoir rock physics, petro‐acoustic data and seismic modelling. A seismic model of flow simulation using fluid substitution concluded that time‐lapse surface seismic or conventional 4D seismic is unlikely to detect the floodfront within the repeatability of surface seismic measurements. Thus, an alternative approach to 4D seismic for reservoir fluid monitoring is proposed. Permanent seismic sensors could be installed in a borehole and on the surface for passive monitoring of microseismic activity from reservoir pore‐pressure perturbations. Reservoir production and injection operations create these pressure or stress perturbations. Reservoir heterogeneities affecting the fluid flow could be mapped by recording the distribution of epicentre locations of these microseisms or small earthquakes. The permanent borehole sensors could also record repeated offset vertical seismic profiling surveys using a surface source at a fixed location to ensure repeatability. The repeated vertical seismic profiling could image the change in reservoir properties with production.     

The reflection of plane waves in a poroelastic half-space saturated with inviscid fluid

This paper discusses surface displacements, surface strain, rocking, and energy partitioning during reflection-of-plane waves in a fluid-saturated poroelastic half-space. The medium is modeled by Biot's theory, and is assumed to be saturated with inviscid fluid. A linear porosity-modulus relation based on experimental data on sandstones is used to determine the material parameters for Biot's model. Numerical results in terms of angle of incident waves and Poisson's ratio are illustrated for various porosities and degrees of solid frame stiffness. The results show that the amount of solid frame stiffness controls the response of a fluid-saturated porous system. A poroelastic medium with essentially dry-frame stiffness behaves like an elastic medium, and the influence of pore fluid increases as dry-frame stiffness is reduced. The effects of a second P-wave become noticeable in poroelastic media with low dry-frame stiffness.     

岩石孔隙结构的地震信号特征

岩石孔隙结构是控制砂岩和碳酸盐岩的地震波速度和渗透率的重要参数之一。如果两种类似的岩石其孔隙度一定,而渗透率不同,那么它们的声波速度相差2km/s,而渗透率两者则可能相差近6个数量级,即从0.01mD到20mO。在本文中我们总结了由一个广义孔隙弹性理论简化的一个双参数弹性速度模型，以描述孔隙结构对弹性波的影响。由于矿物和储层的流体是给定的,我们用孔隙度和骨架的柔性(挠性)因子来确定速度模型,这个模型可以用于地震反演和储层表征,已改善孔隙度和储量的计算骨架柔性因子可用于岩石结构(PST)类型的定量分类,并可以利用叠前、叠后的两种地震资料将其与孔隙的连通性和渗透率联系起来。本项研究同时也有助于说明为什么振幅与偏移距(AVO)分析用于流体检测在某些情况下失败。这是由于孔隙结构对地震波的影响能够掩盖所有流体效应，特别是在碳酸岩中。     

基于非饱和多孔隙介质BISQ模型的储层参数反演

Biot流动和喷射流动是含流体多孔隙介质中流体流动的两种重要力学机制．文中基于同时包含这两种力学机制的非饱和多孔隙BISQ模型,利用小生境遗传算法实现了储层参数(孔隙度、渗透率、含流体饱和度等)的反演．结果表明,本文方法在储层参数的反演过程中目标函数收敛快、且具有较强的抗“噪声”干扰性能,当观测噪声ε≤5%时,储层参数的反演精度很高．最后,通过实测数据的反演应用验证了该方法处理储层参数反演问题的有效性和非饱和BISQ模型的准确性．     

Seismic wave attenuation in fluid-saturated porous media

Contrary to the traditional view, seismic attenuation in Biot's theory of fluid-saturated porous media is due to viscous damping of local (not global) pore-fluid motion. Since substantial inhomogeneities in fluid permeability of porous geological materials are to be expected, the regions of highest local permeability contribute most to the wave energy dissipation while those of lowest permeability dominate the fluid flow rate if they are uniformly distributed. This dichotomy can explain some of the observed discrepancies between computed and measured attenuation of compressional and shear waves in porous earth. One unfortunate consequence of this result is the fact that measured seismic wave attenuation in fluid-filled geological materials cannot be used directly as a diagnostic of the global fluid-flow permeability.     

随机弹性介质中地震波散射衰减分析(英文)

地震波衰减一直是许多学科研究的热点,因为可以反映介质的特性。导致地震波衰减的因素很多,如:传播过程中由于能量扩散导致的几何衰减,固体岩石内部晶粒间相对滑移导致的摩擦衰减,岩石结构不均匀引起的地震波散射衰减。本文主要从统计的观点出发,通过多次数值模拟的方法研究纵波散射在随机弹性介质中所引发的衰减。首先用随机理论建立了二维空间随机弹性介质模型,然后用错格伪谱法的数值方法模拟了波在随机介质中的传播,再通过波场中虚拟检波器的记录,用谱比法估计了弹性波在随机介质中的散射衰减。不同非均匀程度随机弹性介质中的数值结果表明:介质不均匀程度越高,散射衰减越大;在散射体尺寸小于波长的前提下,不同散射体尺寸的计算结果说明:散射体尺寸越大,弹性波衰减越明显。最后提出了一种不均匀孔隙介质中流体流动衰减的方法。通过对随机孔隙介质中地震波的总衰减和散射衰减分别进行了计算,并定量得出了随机孔隙介质中流体流动衰减,结果表明:在实际地震频段下,当介质不均匀尺度101米量级时,散射衰减比流体流动衰减要大,散射衰减是地震波在实际不均匀岩石孔隙介质中衰减的主要原因。     

Quantitative assessment of the complexity of geological structures in terms of seismic propagators

How a wave interacts with heterogeneous media has been pursued by many geophysicists.The complexity of subsurface heterogeneities is seismologically a relative concept to wavelengths of seismic waves.A growing perception is that velocity variations,propagation angles,and computational accuracies are closely related at a variety of scales.A tentative strategy to quantitatively evaluate the complexity of subsurface heterogeneous media is presented in this article to see what scales of geological heterogeneiti...     

Seismic dispersion and attenuation in layered porous rocks with fractures of varying orientations

Wave‐induced fluid flow plays an important role in affecting the seismic dispersion and attenuation of fractured porous rocks. While numerous theoretical models have been proposed for the seismic dispersion and attenuation in fractured porous rocks, most of them neglect the wave‐induced fluid flow resulting from the background anisotropy (e.g. the interlayer fluid flow between different layers) that can be normal in real reservoirs. Here, according to the theories of poroelasticity, we present an approach to study the frequency‐dependent seismic properties of more realistic and complicated rocks, i.e. horizontally and periodically layered porous rock with horizontal and randomly orienting fractures, respectively, distributed in one of the two periodical layers. The approach accounts for the dual effects of the wave‐induced fluid flow between the fractures and the background pores and between different layers (the interlayer fluid flow). Because C₃₃ (i.e., the modulus of the normally incident P‐wave) is directly related to the P‐wave velocity widely measured in the seismic exploration, and its comprehensive dispersion and attenuation are found to be most significant, we study mainly the effects of fracture properties and the stiffness contrast between the different layers on the seismic dispersion and attenuation of C₃₃. The results show that the increasing stiffness contrast enhances the interlayer fluid flow of the layered porous rocks with both horizontal and randomly orienting fractures and weakens the wave‐induced fluid flow between the fractures and the background pores, especially for the layered porous rock with horizontal fractures. The modelling results also demonstrate that for the considered rock construction, the increasing fracture density reduces the interlayer fluid flow while improves the dispersion and attenuation in the fracture‐relevant frequency band. Increasing fracture aspect ratio is found to reduce the dispersion and attenuation in the fracture‐relevant frequency band only, especially for the layered porous rock with horizontal fractures.     

有效应力变化对致密砂岩孔隙结构及弹性波响应的影响规律

致密砂岩气藏具有裂缝发育和有效应力高的特征,研究不同有效压力下孔、裂隙介质地震波传播特征,有利于地震解释与地下储层的识别.但是前人的研究较少考虑岩石内部微观孔隙结构特征与孔隙、裂隙间流体流动的关系.本文首先通过选取四川盆地典型致密砂岩岩样,在不同有效压力下对岩石样本进行超声波实验测量.然后基于实验测得的纵、横波速度进行裂隙参数反演,得到不同有效压力下致密砂岩样本的裂隙孔隙度.再将裂隙孔隙度和样本岩石物理参数代入双重孔隙介质模型,模拟得到不同有效压力下饱水致密砂岩样本纵横波速度频散和衰减的变化规律.结果表明模型预测的速度频散曲线与纵波速度实验测量结果能够较好的吻合.最后统计分析了致密砂岩裂隙参数,得到了致密砂岩储层裂隙参数随有效压力及孔隙度变化特征.依据实际岩石物理参数建立模型,其裂隙参数三维拟合结果能够较好描述致密砂岩裂隙结构与孔隙度、应力的关联,可为实际地震勘探中预测储层裂缝性质提供基础依据.