Numerical estimation of carbonate rock properties using multiscale images

Characterizing the pore space of rock samples using three‐dimensional (3D) X‐ray computed tomography images is a crucial step in digital rock physics. Indeed, the quality of the pore network extracted has a high impact on the prediction of rock properties such as porosity, permeability and elastic moduli. In carbonate rocks, it is usually very difficult to find a single image resolution which fully captures the sample pore network because of the heterogeneities existing at different scales. Hence, to overcome this limitation a multiscale analysis of the pore space may be needed. In this paper, we present a method to estimate porosity and elastic properties of clean carbonate (without clay content) samples from 3D X‐ray microtomography images at multiple resolutions. We perform a three‐phase segmentation to separate grains, pores and unresolved porous phase using 19 μm resolution images of each core plug. Then, we use images with higher resolution (between 0.3 and 2 μm) of microplugs extracted from the core plug samples. These subsets of images are assumed to be representative of the unresolved phase. We estimate the porosity and elastic properties of each sample by extrapolating the microplug properties to the whole unresolved phase. In addition, we compute the absolute permeability using the lattice Boltzmann method on the microplug images due to the low resolution of the core plug images. In order to validate the results of the numerical simulations, we compare our results with available laboratory measurements at the core plug scale. Porosity average simulations for the eight samples agree within 13%. Permeability numerical predictions provide realistic values in the range of experimental data but with a higher relative error. Finally, elastic moduli show the highest disagreements, with simulation error values exceeding 150% for three samples.     

Joint elastic‐electrical properties of reservoir sandstones and their relationships with petrophysical parameters

We measured in the laboratory ultrasonic compressional and shear‐wave velocity and attenuation (0.7–1.0 MHz) and low‐frequency (2 Hz) electrical resistivity on 63 sandstone samples with a wide range of petrophysical properties to study the influence of reservoir porosity, permeability and clay content on the joint elastic‐electrical properties of reservoir sandstones. P‐ and S‐wave velocities were found to be linearly correlated with apparent electrical formation factor on a semi‐logarithmic scale for both clean and clay‐rich sandstones; P‐ and S‐wave attenuations showed a bell‐shaped correlation (partial for S‐waves) with apparent electrical formation factor. The joint elastic‐electrical properties provide a way to discriminate between sandstones with similar porosities but with different clay contents. The laboratory results can be used to estimate sandstone reservoir permeability from seismic velocity and apparent formation factor obtained from co‐located seismic and controlled source electromagnetic surveys.     

Improved understanding of velocity–saturation relationships using 4D computer-tomography acoustic measurements

A recently developed laboratory method allows for simultaneous imaging of fluid distribution and measurements of acoustic‐wave velocities during flooding experiments. Using a specially developed acoustic sample holder that combines high pressure capacity with good transparency for X‐rays, it becomes possible to investigate relationships between velocity and fluid saturation at reservoir stress levels. High‐resolution 3D images can be constructed from thin slices of cross‐sectional computer‐tomography scans (CT scans) covering the entire rock‐core volume, and from imaging the distribution of fluid at different saturation levels. The X‐ray imaging clearly adds a new dimension to rock‐physics measurements; it can be used in the explanation of variations in measured velocities from core‐scale heterogeneities. Computer tomography gives a detailed visualization of density regimes in reservoir rocks within a core. This allows an examination of the interior of core samples, revealing inhomogeneities, porosity and fluid distribution. This mapping will not only lead to an explanation of acoustic‐velocity measurements; it may also contribute to an increased understanding of the fluid‐flow process and gas/liquid mixing mechanisms in rock. Immiscible and miscible flow in core plugs can be mapped simultaneously with acoustic measurements. The effects of core heterogeneity and experimentally introduced effects can be separated, to clarify the validity of measured velocity relationships.     

Effect of sub‐core scale heterogeneities on acoustic and electrical properties of a reservoir rock: a CO2 flooding experiment of brine saturated sandstone in a computed tomography scanner

The effect of sub‐core scale heterogeneity on fluid distribution pattern, and the electrical and acoustic properties of a typical reservoir rock was studied by performing drainage and imbibition flooding tests with CO₂ and brine in a laboratory. Moderately layered Rothbach sandstone was used as a test specimen. Two core samples were drilled; one perpendicular and the other parallel to the layering to allow injection of fluids along and normal to the bedding plane. During the test 3D images of fluid distribution and saturation levels were mapped by an industrial X‐ray CT‐scanner together with simultaneous measurement of electrical resistivity, ultrasonic velocities as well as amplitudes. The results showed how the layering and the flooding direction influenced the fluid distribution pattern and the saturation level of the fluids. For a given fluid saturation level, the measured changes in the acoustic and electrical parameters were affected by both the fluid distribution pattern and the layering orientation relative to the measurement direction. The P‐wave amplitude and the electrical resistivity were more sensitive to small changes in the fluid distribution patterns than the P‐wave velocity. The change in amplitude was the most affected by the orientation of the layering and the resulting fluid distribution patterns. In some instances the change due to the fluid distribution pattern was higher than the variation caused by the change in CO₂ saturation. As a result the Gassmann relation based on ‘uniform' or ‘patchy' saturation pattern was not suitable to predict the P‐wave velocity variation. Overall, the results demonstrate the importance of core‐imaging to improve our understanding of fluid distribution patterns and the associated effects on measured rock‐physics properties.     

基于气体包裹体模型的低孔低渗储层声波速度研究

随着石油勘探工业的持续发展和技术水平的日益提高,低孔低渗油气藏已成为我国油气勘探开发的重要领域之一,但是该类油气藏的储层岩石物理关系复杂,对其评价也相对较难。本文针对中深层气藏低孔低渗储层评价存在的困难,采用修正的White气体包裹体模型开展岩石物理研究。首先对气体包裹体模型进行分析,得到纵横波速度的计算公式,进而理论计算并分析纵横波速度与孔隙度、饱和度、压力及温度参数的变化关系,最后结合岩心实验对理论计算结果进行了验证。研究结果表明基于气体包裹体模型的理论计算结果与实测数据吻合较好,可以较好地为低孔低渗复杂储层声波速度测量及解释提供技术支持。      

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.     

基于计算岩石物理方法的页岩储层弹性参数提取

发展了应用数值计算方法获取页岩储层的速度、各向异性参数的计算岩石物理系列方法.该系列方法包括了大尺度精细地质模型数值建模、计算网格尺度的地球物理建模和地震波数值模拟提取岩石物理弹性参数.本文方法利用储层的统计数据而不是具体岩心的测量数据,可获得储层岩石物理弹性参数的变化规律.相比于基于岩心测试的岩石物理方法,本文方法可精细考虑实际储层的非均匀特征,可得到岩心测试难以求取的与尺寸效应高度相关的弹性参数,也避免了求取弹性参数变化规律时获取不同地质特征岩心的困难.本文发展了计算岩石物理方法,为计算岩石物理面临的大尺度地质建模和计算能力限制问题提供了有效的解决方案.文中以胜利罗家的页岩储层为例,求得了储层TOC含量从3%到21%变化情况下储层的P波、S波速度以及各向异性参数变化规律.     

Multiscale rock-physics templates for gas detection in carbonate reservoirs

The heterogeneous distribution of fluids in patchy-saturated rocks generates significant velocity dispersion and attenuation of seismic waves. The mesoscopic Biot–Rayleigh theory is used to investigate the relations between wave responses and reservoir fluids. Multiscale theoretical modeling of rock physics is performed for gas/water saturated carbonate reservoirs. Comparisons with laboratory measurements, log and seismic data validate the rock physics template. Using post-stack and pre-stack seismic inversion, direct estimates of rock porosity and gas saturation of reservoirs are obtained, which are in good agreement with oil production tests of the wells.     

Joint elastic‐electrical effective medium models of reservoir sandstones

Improvements in the joint inversion of seismic and marine controlled source electromagnetic data sets will require better constrained models of the joint elastic‐electrical properties of reservoir rocks. Various effective medium models were compared to a novel laboratory data set of elastic velocity and electrical resistivity (obtained on 67 reservoir sandstone samples saturated with 35 g/l brine at a differential pressure of 8 MPa) with mixed results. Hence, we developed a new three‐phase effective medium model for sandstones with pore‐filling clay minerals based on the combined self‐consistent approximation and differential effective medium model. We found that using a critical porosity of 0.5 and an aspect ratio of 1 for all three components, the proposed model gave accurate model predictions of the observed magnitudes of P‐wave velocity and electrical resistivity and of the divergent trends of clean and clay‐rich sandstones at higher porosities. Using only a few well‐constrained input parameters, the new model offers a practical way to predict in situ porosity and clay content in brine saturated sandstones from co‐located P‐wave velocity and electrical resistivity data sets.     

Experimental verification of the fracture density and shear‐wave splitting relationship using synthetic silica cemented sandstones with a controlled fracture geometry

We present laboratory ultrasonic measurements of shear‐wave splitting from two synthetic silica cemented sandstones. The manufacturing process, which enabled silica cementation of quartz sand grains, was found to produce realistic sandstones of average porosity 29.7 ± 0.5% and average permeability 29.4 ± 11.3 mD. One sample was made with a regular distribution of aligned, penny‐shaped voids to simulate meso‐scale fractures in reservoir rocks, while the other was left blank. Ultrasonic shear waves were measured with a propagation direction of 90° to the coincident bedding plane and fracture normal. In the water saturated blank sample, shear‐wave splitting, the percentage velocity difference between the fast and slow shear waves, of <0.5% was measured due to the bedding planes (or layering) introduced during sample preparation. In the fractured sample, shear‐wave splitting (corrected for layering anisotropy) of 2.72 ± 0.58% for water, 2.80 ± 0.58% for air and 3.21 ± 0.58% for glycerin saturation at a net pressure of 40 MPa was measured. Analysis of X‐ray CT scan images was used to determine a fracture density of 0.0298 ± 0.077 in the fractured sample. This supports theoretical predictions that shear‐wave splitting (SWS) can be used as a good estimate for fracture density in porous rocks (i.e., SWS = 100ε_f, where ε_f is fracture density) regardless of pore fluid type, for wave propagation at 90° to the fracture normal.     

Quantitative geophysical pore‐type characterization and its geological implication in carbonate reservoirs

This paper discusses and addresses two questions in carbonate reservoir characterization: how to characterize pore‐type distribution quantitatively from well observations and seismic data based on geologic understanding of the reservoir and what geological implications stand behind the pore‐type distribution in carbonate reservoirs. To answer these questions, three geophysical pore types (reference pores, stiff pores and cracks) are defined to represent the average elastic effective properties of complex pore structures. The variability of elastic properties in carbonates can be quantified using a rock physics scheme associated with different volume fractions of geophysical pore types. We also explore the likely geological processes in carbonates based on the proposed rock physics template. The pore‐type inversion result from well log data fits well with the pore geometry revealed by a FMI log and core information. Furthermore, the S‐wave prediction based on the pore‐type inversion result also shows better agreement than the Greensberg‐Castagna relationship, suggesting the potential of this rock physics scheme to characterize the porosity heterogeneity in carbonate reservoirs. We also apply an inversion technique to quantitatively map the geophysical pore‐type distribution from a 2D seismic data set in a carbonate reservoir offshore Brazil. The spatial distributions of the geophysical pore type contain clues about the geological history that overprinted these rocks. Therefore, we analyse how the likely geological processes redistribute pore space of the reservoir rock from the initial depositional porosity and in turn how they impact the reservoir quality.     

泥质含量及其分布形式对岩电关系影响的数字岩心仿真(英文)

由于泥质所造成的附加导电现象,泥质含量及其分布形式对电阻率增大系数I和含水饱和度Sw关系具有重要影响,由于岩石物理实验中岩心孔隙结构及其组分构成、分布的微观不可调性,因而泥质分布形式所造成的影响很难通过岩心实验来单独研究。基于数字岩心的格子气自动机方法是一种有效的微观数值模拟方法,本研究利用储层岩心薄片的骨架颗粒尺寸信息资料建立数字岩心模型,结合格子气自动机技术对数字岩心不同饱和流体情况下电的传输特性进行数值模拟研究,揭示了不同泥质含量和泥质分布形式对孔隙介质导电特性非阿尔奇现象产生的影响,建立饱和度指数和泥质含量之间的关系模型,其良好的吻合性表明该方法在岩石物理研究中是一种十分有效的研究方法,而新模型适于在非阿尔奇储层进行准确的饱和度评价。     

Influence of crack distribution of rocks on P‐wave velocity anisotropy – a laboratory and field scale study‡

The purpose of this paper is the comparison of P‐wave velocity and velocity anisotropy, measured at different scales under laboratory and field conditions. A shallow seismic refraction survey with shot/receiver spacing of up to 10 m was carried out on a flat outcrop of lhertzolite in the southern part of the Balmuccia massif. Oriented rock samples were also obtained from the locality. The particular advantage of the laboratory method used is the possibility of measuring velocity in any direction under controlled conditions. Laboratory tests were made on spherical peridotite samples, 50 mm in diameter, by ultrasonic velocity measurements in 132 directions (meridian and parallel networks) under confining stress ranging from atmospheric to 400 MPa. The mean P‐wave velocity of the field and laboratory data differed by between 20–30%. In addition, P‐wave velocity anisotropy of 25% was detected in the field data. Whereas the anisotropy in the laboratory samples in the same orientation as the field surveys was less than 2%. This observed scaling factor is related to the different sampling sizes and the difference in frequencies of applied elastic waves. With an ultrasonic wavelength of 10 mm, laboratory samples represent a continuum. The field velocities and velocity anisotropy reflect the presence of cracks, which the laboratory rock samples do not contain. Three sub‐vertical fracture sets with differing strikes were observed in the field outcrop. Estimates of fracture stiffness from the velocity anisotropy data are consistent with other published values. These results highlight the difficulty of using laboratory velocity estimates to interpret field data.     

泥质砂岩中接触胶结泥质定量估算及对砂岩弹性的影响

在泥质砂岩的岩石物理建模中,明确泥质砂岩中泥质胶结物的接触类型及其含量对正确认识泥质的胶结作用对泥质砂岩声速的影响以及合理地建立岩石物理模型至关重要.现阶段,尚未有实验室定量估算胶结泥质的方法,导致应用胶结砂岩理论模型预测胶结砂岩地层的声速时往往由于胶结物含量被高估从而导致预测声速结果偏高.本文通过观察铸体薄片中泥质与颗粒之间的接触关系和相对分布提出了一种区分胶结泥质和分散泥质的方法:与两个或两个以上颗粒接触的连续分布的泥质为胶结泥质;与一个颗粒接触或者不与颗粒接触的泥质为分散泥质.基于这一准则,本文基于像素拾取法估算了人造泥质砂岩的胶结泥质含量,并将胶结泥质含量作为胶结砂岩模型的输入参数优化CCT模型.对比原始模型,本文方法声速误差下降了20%,预测准确度显著提高.本文方法适用于弱胶结地层的岩石物理建模,能够准确的预测声速以结合地震和测井资料识别有利储层,定量评价储层参数.     

Estimating azimuthal stress‐induced P‐wave anisotropy from S‐wave anisotropy using sonic log or vertical seismic profile data

Most sedimentary rocks are anisotropic, yet it is often difficult to accurately incorporate anisotropy into seismic workflows because analysis of anisotropy requires knowledge of a number of parameters that are difficult to estimate from standard seismic data. In this study, we provide a methodology to infer azimuthal P‐wave anisotropy from S‐wave anisotropy calculated from log or vertical seismic profile data. This methodology involves a number of steps. First, we compute the azimuthal P‐wave anisotropy in the dry medium as a function of the azimuthal S‐wave anisotropy using a rock physics model, which accounts for the stress dependency of seismic wave velocities in dry isotropic elastic media subjected to triaxial compression. Once the P‐wave anisotropy in the dry medium is known, we use the anisotropic Gassmann equations to estimate the anisotropy of the saturated medium. We test this workflow on the log data acquired in the North West Shelf of Australia, where azimuthal anisotropy is likely caused by large differences between minimum and maximum horizontal stresses. The obtained results are compared to azimuthal P‐wave anisotropy obtained via orthorhombic tomography in the same area. In the clean sandstone layers, anisotropy parameters obtained by both methods are fairly consistent. In the shale and shaly sandstone layers, however, there is a significant discrepancy between results since the stress‐induced anisotropy model we use is not applicable to rocks exhibiting intrinsic anisotropy. This methodology could be useful for building the initial anisotropic velocity model for imaging, which is to be refined through migration velocity analysis.     

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

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

岩石物理模版在储层定量解释中的应用

岩石物理模板采用测井解释的各类岩性矿物骨架点值,选取适合该地区的岩石物理模型,模拟在不同储层组合、不同孔隙及不同饱和度情况下,储层岩石物理参数变化引起的储层测井参数及地球物理响应特征的变化,定量地建立起储层参数同地球物理弹性参数间的解释关系模版.本文根据新场JS42气藏储层参数分析结果,尝试性地将岩石物理解释模板应用于储层定量解释中,对储层高产气区、含水区域进行定量解释,并预测了该气藏的气水界面,该预测结果与实钻井测试情况吻合,证实了该方法的科学性.     

Pore fluid viscosity effects on P‐ and S‐wave anisotropy in synthetic silica‐cemented sandstone with aligned fractures

Ultrasonic (500 kHz) P‐ and S‐wave velocity and attenuation anisotropy were measured in the laboratory on synthetic, octagonal‐shaped, silica‐cemented sandstone samples with aligned penny‐shaped voids as a function of pore fluid viscosity. One control (blank) sample was manufactured without fractures, another sample with a known fracture density (measured from X‐ray CT images). Velocity and attenuation were measured in four directions relative to the bedding fabric (introduced during packing of successive layers of sand grains during sample construction) and the coincident penny‐shaped voids (fractures). Both samples were measured when saturated with air, water (viscosity 1 cP) and glycerin (100 cP) to reveal poro‐visco‐elastic effects on velocity and attenuation, and their anisotropy. The blank sample was used to estimate the background anisotropy of the host rock in the fractured sample; the bedding fabric was found to show transverse isotropy with shear wave splitting (SWS) of 1.45 ± 1.18% (i.e. for S‐wave propagation along the bedding planes). In the fractured rock, maximum velocity and minimum attenuation of P‐waves was seen at 90° to the fracture normal. After correction for the background anisotropy, the fractured sample velocity anisotropy was expressed in terms of Thomsen's weak anisotropy parameters ε, γ & δ. A theory of frequency‐dependent seismic anisotropy in porous, fractured, media was able to predict the observed effect of viscosity and bulk modulus on ε and δ in water‐ and glycerin‐saturated samples, and the higher ε and δ values in air‐saturated samples. Theoretical predictions of fluid independent γ are also in agreement with the laboratory observations. We also observed the predicted polarisation cross‐over in shear‐wave splitting for wave propagation at 45° to the fracture normal as fluid viscosity and bulk modulus increases.     

地震岩石物理研究进展

地震岩石物理(Seismic Rock Physics)是研究岩石物理性质与地震响应之间关系的一门学科,旨在通过研究不同温度压力条件下岩性、孔隙度、孔隙流体等对岩石弹性性质的影响,分析地震波传播规律,建立各岩性参数、物性参数与地震速度、密度等弹性参数之间的关系.本文主要论述了半个多世纪以来,国内外地震岩石物理在岩石、流体基础研究、烃类检测等方面取得的主要进展,并分析目前国内岩石物理的研究现状、存在的问题、最新研究动向及展望.     

3D imaging of a reservoir analogue in point bar deposits in the Ferron Sandstone, Utah, using ground-penetrating radar

Most existing reservoir models are based on 2D outcrop studies; 3D aspects are inferred from correlation between wells, and so are inadequately constrained for reservoir simulations. To overcome these deficiencies, we have initiated a multidimensional characterization of reservoir analogues in the Cretaceous Ferron Sandstone in Utah. Detailed sedimentary facies maps of cliff faces define the geometry and distribution of reservoir flow units, barriers and baffles at the outcrop. High‐resolution 2D and 3D ground‐penetrating radar (GPR) images extend these reservoir characteristics into 3D to allow the development of realistic 3D reservoir models. Models use geometric information from mapping and the GPR data, combined with petrophysical data from surface and cliff‐face outcrops, and laboratory analyses of outcrop and core samples. The site of the field work is Corbula Gulch, on the western flank of the San Rafael Swell, in east‐central Utah. The outcrop consists of an 8–17 m thick sandstone body which contains various sedimentary structures, such as cross‐bedding, inclined stratification and erosional surfaces, which range in scale from less than a metre to hundreds of metres. 3D depth migration of the common‐offset GPR data produces data volumes within which the inclined surfaces and erosional surfaces are visible. Correlation between fluid permeability, clay content, instantaneous frequency and instantaneous amplitude of the GPR data provides estimates of the 3D distribution of fluid permeability and clay content.