饱和砂岩在温度和频率域的衰减和速度频散

利用Metravib热机械分析仪, 在天然地震的频率和温度范围内, 首次对泵油和甘油饱和两种孔隙度的彭山砂岩的衰减和速度频散进行了实验研究． 结果表明, ① 泵油饱和彭山砂岩对频率和温度的依赖呈热激活弛豫规律; ② 杨氏模量和弹性波速度与孔隙度、 温度呈负相关, 与饱和液体的黏滞系数、 频率呈正相关; ③ 频散效应因频率上升而增强, 因温度增高而减弱． 这一规律性的结果为地震波理论研究提供了实验基础．     

Seismic attenuation and velocity dispersion in fractured rocks: The role played by fracture contact areas

The presence of fractures in fluid‐saturated porous rocks is usually associated with strong seismic P‐wave attenuation and velocity dispersion. This energy dissipation can be caused by oscillatory wave‐induced fluid pressure diffusion between the fractures and the host rock, an intrinsic attenuation mechanism generally referred to as wave‐induced fluid flow. Geological observations suggest that fracture surfaces are highly irregular at the millimetre and sub‐millimetre scale, which finds its expression in geometrical and mechanical complexities of the contact area between the fracture faces. It is well known that contact areas strongly affect the overall mechanical fracture properties. However, existing models for seismic attenuation and velocity dispersion in fractured rocks neglect this complexity. In this work, we explore the effects of fracture contact areas on seismic P‐wave attenuation and velocity dispersion using oscillatory relaxation simulations based on quasi‐static poroelastic equations. We verify that the geometrical and mechanical details of fracture contact areas have a strong impact on seismic signatures. In addition, our numerical approach allows us to quantify the vertical solid displacement jump across fractures, the key quantity in the linear slip theory. We find that the displacement jump is strongly affected by the geometrical details of the fracture contact area and, due to the oscillatory fluid pressure diffusion process, is complex‐valued and frequency‐dependent. By using laboratory measurements of stress‐induced changes in the fracture contact area, we relate seismic attenuation and dispersion to the effective stress. The corresponding results do indeed indicate that seismic attenuation and phase velocity may constitute useful attributes to constrain the effective stress. Alternatively, knowledge of the effective stress may help to identify the regions in which wave induced fluid flow is expected to be the dominant attenuation mechanism.     

储层岩石流动电位频散特性的数学模拟

利用储层岩石流动电位的频散特性评价复杂储层已经成为勘探地球物理领域关注的热点,但是目前还没有形成基于储层岩石储渗特性及电化学性质的具有普遍指导意义的理论方法和数学模型.本文利用微观毛管理论,通过随时间谐变条件下渗流场和电流场的耦合模型,建立了描述储层岩石流动电位频散特性的数学方法,定量分析了频率域储层岩石动态渗透率、动电耦合系数和流动电位耦合系数随储层岩石孔隙度、溶液浓度和阳离子交换量的变化规律.研究结果表明:储层岩石流动电位频散特性是储层流体惯性力与流体黏滞力相互作用的结果.储层岩石孔隙度越大,储层维持流体原有运动状态的能力越大,临界频率越小;储层岩石的溶液浓度和阳离子交换量对临界频率没有影响.储层岩石的孔隙度越大,流体流动能力越强,流动电位各耦合系数的数值越大;溶液浓度越小或阳离子交换量越大,孔隙固液界面的双电层作用越强,各耦合系数的数值越大.     

非饱和岩石中的纵波频散与衰减: 双重孔隙介质波传播方程

本文采用Rayleigh理论描述纵波激励下非饱和岩石中气泡的局域流体流动,从经典力学的哈密顿原理导出了双重孔隙介质中的波传播方程,即Biot-Rayleigh方程.方程的格式简洁,参数少,所有相关参数物理可测,因此,方程具有较好的物理可实现性.基于相同的岩石与前人理论对比,初步验证了本理论的有效性.对三个地区的砂岩储层进行了分析,结果显示:地震频段内纵波对储层是否含气非常敏感,但对含气饱和度指示性不佳,且随着孔隙度降低,纵波频散与衰减在中低频段更为显著;含甲烷与含二氧化碳的砂岩储层均呈第三类AVO响应特征,很难从叠前分析技术中鉴别;理论预测的纵波频散随饱和度与频率变化的趋势与特征,与多频段实验观测结果一致.     

Attenuation mechanisms in fractured fluid-saturated porous rocks: a numerical modelling study

Seismic attenuation mechanisms receive increasing attention for the characterization of fractured formations because of their inherent sensitivity to the hydraulic and elastic properties of the probed media. Attenuation has been successfully inferred from seismic data in the past, but linking these estimates to intrinsic rock physical properties remains challenging. A reason for these difficulties in fluid-saturated fractured porous media is that several mechanisms can cause attenuation and may interfere with each other. These mechanisms notably comprise pressure diffusion phenomena and dynamic effects, such as scattering, as well as Biot's so-called intrinsic attenuation mechanism. Understanding the interplay between these mechanisms is therefore an essential step for estimating fracture properties from seismic measurements. In order to do this, we perform a comparative study involving wave propagation modelling in a transmission set-up based on Biot's low-frequency dynamic equations and numerical upscaling based on Biot's consolidation equations. The former captures all aforementioned attenuation mechanisms and their interference, whereas the latter only accounts for pressure diffusion phenomena. A comparison of the results from both methods therefore allows to distinguish between dynamic and pressure diffusion phenomena and to shed light on their interference. To this end, we consider a range of canonical models with randomly distributed vertical and/or horizontal fractures. We observe that scattering attenuation strongly interferes with pressure diffusion phenomena, since the latter affect the elastic contrasts between fractures and their embedding background. Our results also demonstrate that it is essential to account for amplitude reductions due to transmission losses to allow for an adequate estimation of the intrinsic attenuation of fractured media. The effects of Biot's intrinsic mechanism are rather small for the models considered in this study.     

基于电震耦合理论研究电极法储层岩石复电阻率频散特性

复电阻率测井在识别油水层的能力上优于常规电阻率测井,然而储层岩石复电阻率特性的微观机理还没有统一完整的解释和数学模拟方法,致使复电阻率测井技术的开发缺乏足够的理论基础.本文基于孔隙介质Pride电震耦合理论,结合谐变信号激励下渗流场与电流场的耦合理论,推导出一级近似条件下的Pride电震耦合理论.采用格林函数方法建立了一维电震波场的波动方程及其解.构造了双电极法测量储层岩石复电阻率的物理模型和数学模型,从理论上阐明了岩石复电阻率频散特性的微观机制与电震效应的关系,定量分析了储层岩石复电阻率频散特性的影响因素.数学模拟结果表明:储层岩石复电阻率的频散现象是在电震快纵波和电震慢纵波的共同作用下,由孔隙介质中的电渗流机制形成的;储层岩石的复电阻率随孔隙度的增大而减小,随渗透率的增大而增大,地层水矿化度的增加或阳离子交换量的增大使得同频率的复电阻率减小.慢纵波界面极化频率受孔隙度、渗透率和地层弹性模量的影响较大,而快纵波界面极化频率受地层弹性模量的影响较大.     

Pore pressure profiles in fractured and compliant rocks1

Fluid permeability in fractured rocks is sensitive to pore-pressure changes. This dependence can have large effects on the flow of fluids through rocks. We define the permeability compliance γ= 1/k(k/δp_p)_pc, which is the sensitivity of the permeability k to the pore pressure p_p at a constant confining pressure p_c, and solve the specific problems of constant pressure at the boundary of a half-space, a cylindrical cavity and a spherical cavity. The results show that when the magnitude of permeability compliance is large relative to other compliances, diffusion is masked by a piston-like pressure profile. We expect this phenomenon to occur in highly fractured and compliant rock systems where γ may be large. The pressure profile moves rapidly when fluids are pumped into the rock and very slowly when fluids are pumped out. Consequently, fluid pressure, its history and distribution around injection and production wells may be significantly different from pressures predicted by the linear diffusion equation. The propagation speed of the pressure profile, marked by the point where δp_p/δx is a maximum, decreases with time approximately as and the amplitude of the profile also dissipates with time (or distance). The effect of permeability compliance can be important for fluid injection into and withdrawal from reservoirs. For example, excessive drawdown could cause near-wellbore flow suffocation. Also, estimates of the storage capacity of reservoirs may be greatly modified when γ is large. The large near-wellbore pressure gradients caused during withdrawal by large γ can cause sanding and wellbore collapse due to excessive production rates.     

Small-scale electrical resistivity tomography of wet fractured rocks

This paper describes a series of experiments that tested the ability of the electrical resistivity tomography (ERT) method to locate correctly wet and dry fractures in a meso-scale model. The goal was to develop a method of monitoring the flow of water through a fractured rock matrix. The model was a four by six array of limestone blocks equipped with 28 stainless steel electrodes. Dry fractures were created by placing pieces of vinyl between one or more blocks. Wet fractures were created by injecting tap water into a joint between blocks. In electrical terms, the dry fractures are resistive and the wet fractures are conductive. The quantities measured by the ERT system are current and voltage around the outside edge of the model. The raw ERT data were translated to resistivity values inside the model using a three-dimensional Occam's inversion routine. This routine was one of the key components of ERT being tested. The model presented several challenges. First, the resistivity of both the blocks and the joints was highly variable. Second, the resistive targets introduced extreme changes the software could not precisely quantify. Third, the abrupt changes inherent in a fracture system were contrary to the smoothly varying changes expected by the Occam's inversion routine. Fourth, the response of the conductive fractures was small compared to the background variability. In general, ERT was able to locate correctly resistive fractures. Problems occurred, however, when the resistive fracture was near the edges of the model or when multiple fractures were close together. In particular, ERT tended to position the fracture closer to the model center than its true location. Conductive fractures yielded much smaller responses than the resistive case. A difference-inversion method was able to correctly locate these targets.     

A constitutive model for water flow in unsaturated fractured rocks

A conceptual model for describing effective saturation in fractured hard rock is presented. The fracture network and the rock matrix are considered as an equivalent continuum medium where each fracture is conceptualized as a porous medium of granular structure and the rock matrix is assumed to be impermeable. The proposed model is based on the representation of a rough‐walled fracture by an equivalent porous medium, which is described using classical constitutive models. A simple closed‐form equation for the effective saturation is obtained when the van Genuchten model is used to describe saturation inside fractures and fractal laws are assumed for both aperture and number of fractures. The relative hydraulic conductivity for the fractured rock is predicted from a simple relation derived by Liu and Bodvarsson. The proposed constitutive model contains three independent parameters, which may be obtained by fitting the proposed effective saturation curve to experimental data. Two of the model parameters have physical meaning and can be identified with the reciprocal of the air entry pressure values in the fractures of minimum and maximum apertures. Effective saturation and relative hydraulic conductivity curves match fairly well the simulated constitutive relations obtained by Liu and Bodvarsson. Copyright © 2008 John Wiley & Sons, Ltd.     

基于两级尺度粗化的裂缝-多孔隙介质地震响应分析方法

实际地震勘探中,储层物性参数的差异是导致地震波响应特征发生变化的根本原因,而建立储层物性参数与地震响应特征之间的联系,需要跨越微观孔隙尺度、介观测井尺度以及宏观地震尺度等三个不同尺度空间.本文基于已知井的岩石物理实验数据和测井数据,利用复杂多孔隙介质理论将微观尺度孔隙岩石粗化到介观测井尺度,利用Backus平均理论将介观测井尺度的模型进一步粗化到宏观地震尺度,最终,得到地震尺度裂缝-多孔隙介质模型.其数值计算结果与测井数据和地震数据的对比表明：基于两级尺度粗化算法的裂缝多孔隙介质模型在给定参数下是有效的,且基于该模型的地震响应特征分析方法能够对储层的地震响应特征随物性参数的变化进行分析.

     

Anisotropic effective conductivity in fractured rocks by explicit effective medium methods

In this work, we assess the use of explicit methods for estimating the effective conductivity of anisotropic fractured media. Explicit methods are faster and simpler to use than implicit methods but may have a more limited range of validity. Five explicit methods are considered: the Maxwell approximation, the T‐matrix method, the symmetric and asymmetric weakly self‐consistent methods, and the weakly differential method, where the two latter methods are novelly constructed in this paper. For each method, we develop simplified expressions applicable to flat spheroidal “penny‐shaped” inclusions. The simplified expressions are accurate to the first order in the ratio of fracture thickness to fracture diameter. Our analysis shows that the conductivity predictions of the methods fall within known upper and lower bounds, except for the T‐matrix method at high fracture densities and the symmetric weakly self‐consistent method when applied to very thin fractures. Comparisons with numerical results show that all the methods give reliable estimates for small fracture densities. For high fracture densities, the weakly differential method is the most accurate if the fracture geometry is non‐percolating or the fracture/matrix conductivity contrast is small. For percolating conductive fracture networks, we have developed a scaling relation that can be applied to the weakly self‐consistent methods to give conductivity estimates that are close to the results from numerical simulations.     

An equivalent medium model for wave simulation in fractured porous rocks

Seismic wave propagation in reservoir rocks is often strongly affected by fractures and micropores. Elastic properties of fractured reservoirs are studied using a fractured porous rock model, in which fractures are considered to be embedded in a homogeneous porous background. The paper presents an equivalent media model for fractured porous rocks. Fractures are described in a stress‐strain relationship in terms of fracture‐induced anisotropy. The equations of poroelasticity are used to describe the background porous matrix and the contents of the fractures are inserted into a matrix. Based on the fractured equivalent‐medium theory and Biot's equations of poroelasticity, two sets of porosity are considered in a constitutive equation. The porous matrix permeability and fracture permeability are analysed by using the continuum media seepage theory in equations of motion. We then design a fractured porous equivalent medium and derive the modified effective constants for low‐frequency elastic constants due to the presence of fractures. The expressions of elastic constants are concise and are directly related to the properties of the main porous matrix, the inserted fractures and the pore fluid. The phase velocity and attenuation of the fractured porous equivalent media are investigated based on this model. Numerical simulations are performed. We show that the fractures and pores strongly influence wave propagation, induce anisotropy and cause poroelastic behaviour in the wavefields. We observe that the presence of fractures gives rise to changes in phase velocity and attenuation, especially for the slow P‐wave in the direction parallel to the fracture plane.     

Determining the permeability of fractured rocks based on joint mapping

A typical fractured rock mass is intersected by several sets of discontinuities, which provide the main flowpath for ground water. Due to the limitations of data obtained by conventional field measurements, it is often difficult to estimate the anisotropic permeability tensor associated with the joints existing in the rock mass. For that reason, determining permeability tensors for fractured rocks is an important topic in rock mass hydraulics. Based on field surveys, joint parameters can be analyzed by using probabilistic and statistical tools, and three-dimensional mapping of the jointed rock mass. Through analysis of a single joint's hydraulic characteristics, the principal value of the permeability tensor for the jointed rock mass can be determined by using Monte Carlo methods and the searching percolation trace method, which is developed in this paper. The study reports on practical examples demonstrating that results from the methods discussed in this paper are in agreement with those from field hydrogeological surveys and measurements.     

Estimation of snow ablation under a dust layer covering a wide range of albedo

Ablation processes of snow under a thin dust cover are complicated compared with those under a thick cover, mainly owing to the effects of aggregation (redistribution) of dust particles on the conditions of surface melting. Aggregation of dust particles causes the snow surface to brighten after the initial dust configuration, thus affecting the relationship between initial dust concentration and surface albedo. In order to estimate snow ablation rate under a thin dust cover, we used a composite energy balance model in which the surface albedo is taken as a measured input variable. The estimated results of snow ablation agreed reasonably well with the observation, considering the measurement errors inherited in the snow depressions. Comparison of the two cases, that is, one considering the aggregation of dust particles (observation: albedo variable) and the other without aggregation (assumption: albedo constant), showed that the ablation rates were noticeably lower on the former case. This suggests that the aggregation of dust particles induces a reduction of snow ablation. Copyright © 2002 John Wiley & Sons, Ltd.     

Estimation of effective dispersion coefficients in rocks with a regular staggered system of fractures

The influence of rock fracturing on the hydraulic dispersion parameters is studied by numerical simulation. A porous medium with a regular system of parallel cracks is examined as a model of fractured rocks. A fractured-porous medium is conventionally assumed to be locally uniform (within an elementary representative volume of the model), and the presence of heterogeneities is implicitly accounted for by the so-called effective values of the dispersion parameters of an underground medium. The mass transfer is calculated within a broad range of fracturing parameters with separate cracks being explicitly incorporated. The effective values of the dispersion parameters are determined by averaging results of the calculation. The numerically obtained implicit dependence of the effective dispersion parameters on fracturing prameters is approximated by analytical expressions.     

Seismic velocities in fractured rocks: an experimental verification of Hudson's theory1

Flow of fluids in many hydrocarbon reservoirs and aquifers is enhanced by the presence of cracks and fractures. These cracks could be detected by their effects on propagation of compressional and shear waves through the reservoir: several theories, including Hudson's, claim to predict the seismic effects of cracks. Although Hudson's theory has already been used to calculate crack densities from seismic surveys, the predictions of the theory have not yet been tested experimentally on rocks containing a known crack distribution. This paper describes an experimental verification of the theory. The rock used, Carrara marble, was chosen for its uniformity and low porosity, so that the effect of cracks would not be obscured by other influences. Cracks were induced by loading of laboratory specimens. Velocities of compressional and shear waves were measured by ultrasound at 0.85 MHz in dry and water-saturated specimens at high and low effective pressures. The cracks were then counted in polished sections of the specimens. In ‘dry’ specimens with both dry and saturated cracks, Hudson's theory overpredicted observed crack densities by a constant amount that is attributed to the observed value being systematically underestimated. The theory made poor predictions for fully saturated specimens. Shear-wave splitting, caused by anisotropy due to both crystal and crack alignment, was observed. Cracks were seen to follow grain boundaries rather than the direction of maximum compression due to loading. The results demonstrate that Hudson's theory may be used in some cases to determine crack and fracture densities from compressional- and shear-wave velocity data.     

背景为各向异性的含裂缝岩石频散和衰减计算方法研究

裂缝广泛分布于各类储层岩石中, 并且会显著提高储层的渗流能力.因此, 裂缝的评价和表征对于提高油气产能具有重要意义.由于裂缝与背景介质之间的波致流会显著影响地震波的频散和衰减特性, 所以地震勘探是评价裂缝性储层的有效手段.裂缝地震定量表征的前提是要基于含裂缝岩石中波致流对频散和衰减的影响建立含裂缝岩石物理特性与地震性质的关系.然而, 目前相关的理论研究大部分基于各向同性背景这一假设, 难以有效应用于常见的各向异性储层.本文针对背景为各向异性的含裂缝岩石提出了频散和衰减的计算方法.该方法首先将含裂缝岩石中的各向异性背景介质等效为层状背景介质; 然后, 通过分析不同频率下层状含裂缝岩石中的流体压力分布, 理论计算了两个特定的中间频率并求解得到两个中间频率下的弹性参数; 进一步, 以计算得到的两个特定中间频率以及高低频极限下的弹性参数为基础, 应用数值方法求解得到弛豫函数中的未知参数, 最终实现了背景为各向异性含裂缝岩石中频散和衰减的理论模拟.通过将理论预测结果与实验测量和数值模拟结果进行对比, 验证了该方法在背景为各向异性含不同分布裂缝岩石中的有效性.本文提出的方法考虑了常见的各向异性背景对含裂缝岩石频散和衰减的影响, 因而在裂缝性储层的地震勘探中具有广泛的应用前景.

     

P-wave dispersion and attenuation in fractured and porous reservoirs – poroelasticity approach

Natural fractures in hydrocarbon reservoirs can cause significant seismic attenuation and dispersion due to wave induced fluid flow between pores and fractures. We present two theoretical models explicitly based on the solution of Biot's equations of poroelasticity. The first model considers fractures as planes of weakness (or highly compliant and very thin layers) of infinite extent. In the second model fractures are modelled as thin penny-shaped voids of finite radius. In both models attenuation is a result of conversion of the incident compressional wave energy into the diffusive Biot slow wave at the fracture surface and exhibits a typical relaxation peak around a normalized frequency of about 1. This corresponds to a frequency where the fluid diffusion length is of the order of crack spacing for the first model and the crack diameter for the second. This is consistent with an intuitive understanding of the nature of attenuation: when fractures are closely and regularly spaced, the Biot's slow waves produced by cracks interfere with each other, with the interference pattern controlled by the fracture spacing. Conversely, if fractures are of finite length, which is smaller than spacing, then fractures act as independent scatterers and the attenuation resembles the pattern of scattering by isolated cracks. An approximate mathematical approach based on the use of a branching function gives a unified analytical framework for both models.     

Closure relations for mobile bed debris flows in a wide range of slopes and concentrations

Debris flows are flows of water and sediment driven by gravity that initiate in the upper part of a stream, where the slope is very steep, allowing high values of solid concentration (hyperconcentrated flows), and that stop in the lower part of the basin, which is characterized by much lower slopes and reduced speeds and concentrations. Modelling these flows requires mathematical and numerical tools capable of simulating the behavior of a fluid in a wide range of concentrations of the solid phase, spanning from hyperconcentrated flows to flows in the fluvial regime. According to a two-phase approach, the depth integrated equations of mass and momentum conservation for water and sediments, under the shallow water hypothesis, are employed to solve field problems related to debris flows. These equations require suitable closure relations that in this case should be valid in a very wide range of slopes. In the hypothesis of absence of cohesive material, we derived these closure relations properly combining the relative relations valid separately in the fluvial and in the hyperconcentrated regimes. In the intermediate regime, the shear stress is due to the combined effect of the deformation of the liquid phase (grain roughness turbulence) and of inter-particle collisions. Therefore, an approach based on the sum of the effects of the two causes has been proposed, combining the Darcy–Weisbach equation and the Bagnoldian grain-inertia theory.A similar treatment has been made for the transport capacity relations, combing the Bagnold expression of the collisional regime with a transport capacity monomial formula valid in the fluvial regime.The closure relations are expressed in non-dimensional form as a function of the Froude number, of the solid concentration, of the relative submergence, and of the slope.In order to test the closure relation, a set of experiments with mixtures of non-cohesive sediments and water have been carried out in a laboratory flume under steady uniform flow conditions, with different solid and liquid discharges and different grain size distributions. The closure equations are satisfactorily tested against experimental investigation.     

Velocity and attenuation in partially saturated rocks: poroelastic numerical experiments

We use a poroelastic modelling algorithm to compute numerical experiments on wave propagation in a rock sample with partial saturation using realistic fluid distribution patterns from tomography scans. Frequencies are in the range 10 to 500 kHz. The rock is a homogeneous isotropic sandstone partially filled with gas and water, which are defined by their characteristic values of viscosity, compressibility and density. We assume no mixing and that the two different pore-fills occupy different macroscopic regions. The von Kármán self-similar correlation function is used, employing different fractal parameters to model uniform and patchy fluid distributions, respectively, where effective saturation is varied in steps from full gas to full water saturation. Without resorting to additional matrix–fluid interaction mechanisms, we are able to reproduce the main features of the variation in wave velocity and attenuation with effective saturation and frequency, as those of published laboratory experiments. Furthermore, the behaviour of the attenuation peaks versus water saturation and frequency is similar to that of White's model. The conversion of primary P-wave energy into dissipating slow waves at the heterogeneities is shown to be the main mechanism for attenuating the primary wavefield. Fluid/gas patches are shown to affect attenuation more than equivalent patches in the permeability or solid-grain properties.