From noise correlation to resonant ultrasound spectroscopy in rock acoustics

This article introduces an alternative experimental procedure for measuring the elastic properties of a solid material at laboratory scale, using both the principles of passive seismic interferometry and resonance ultrasound spectroscopy. We generate noise into the studied sample with a pneumatic air blow gun, and we cross‐correlate the signals recorded with two passive piezoelectric sensors put in soft contact with the sample surface. Resonance phenomena are induced in the sample, but in contrast with conventional resonance ultrasound spectroscopy experiments, we have no control over the injected frequencies that are sent all together within the noise spectrum. The spectrum of the correlogram is a good approximation of the resonance spectrum of the vibrating sample and can be inverted in terms of the elastic moduli of the constituent material of the sample. The experimental procedure is validated on samples made of standard materials (here, aluminium and Plexiglas) by consistently comparing the inverted elastic velocities with the velocities independently measured with the conventional technique of ultrasonic pulse transmission. Moreover, we got similar positive results on dry rock samples, such as Vilhonneur limestone. These encouraging preliminary results open up promising prospects for monitoring fluid substitution in rock samples using the technique described in this paper.     

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.     

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.     

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.     

Effect of oil composition on fluid substitution in heavy oil reservoirs

Unlike light oils, heavy oils do not have a well‐established scheme for modelling elastic moduli from dynamic reservoir properties. One of the main challenges in the fluid substitution of heavy oils is their viscoelastic nature, which is controlled by temperature, pressure, and fluid composition. Here, we develop a framework for fluid substitution modelling that is reliable yet practical for a wide range of cold and thermal recovery scenarios in producing heavy oils and that takes into account the reservoir fluid composition, grounded on the effective‐medium theories for estimating elastic moduli of an oil–rock system. We investigate the effect of fluid composition variations on oil–rock elastic moduli with temperature changes. The fluid compositional behaviour is determined by flash calculations. Elastic moduli are then determined using the double‐porosity coherent potential approximation method and the calculated viscosity based on the fluid composition. An increase in temperature imposes two opposing mechanisms on the viscosity behaviour of a heavy‐oil sample: gas liberation, which tends to increase the viscosity, and melting, which decreases the viscosity. We demonstrate that melting dominates gas liberation, and as a result, the viscosity and, consequently, the shear modulus of the heavy oils always decrease with increasing temperature. Furthermore, it turns out that one can disregard the effects of gas in the solution when modelling the elastic moduli of heavy oils. Here, we compare oil–rock elastic moduli when the rock is saturated with fluids that have different viscosity levels. The objective is to characterize a unique relation between the temperature, the frequency, and the elastic moduli of an oil–rock system. We have proposed an approach that takes advantage of this relation to find the temperature and, consequently, the viscosity in different regions of the reservoir.     

基于岩石物理模板的孔隙度非敏感流体因子构建方法及应用

流体因子是一种指示储层含流体特征的常用工具,在储层流体识别中发挥着重要作用.现有的大多数流体因子除了反映孔隙流体性质以外还与孔隙度密切相关,对同一储层的高孔和低孔区域具有不同的流体敏感性,可能造成非均质储层的流体识别假象.本文提出一种消除孔隙度影响的流体因子,并将其应用于非均质储层流体识别.首先根据研究区地质特征选择并校准岩石物理模型,以此为基础优选横波阻抗I_S和饱和岩石体积模量与剪切模量之比K_sat/μ_sat构建能够分离岩石骨架和孔隙流体性质的I_S-K_sat/μ_sat岩石物理模板;而后通过对数域多项式拟合和归一化的方式构建孔隙度非敏感流体因子PINF(Porosity-Insensitive Normalized Fluid Factor).最后将本文提出的流体因子应用于苏里格气田非均质储层流体识别,实际测井和地震资料测试结果表明该流体因子的预测结果与测井解释结果相符,在同一储层段的高孔和低孔区域均显现出较好的应用效果,适用于非均质储层流体识别.     

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.     

基于各向异性岩石物理的缝隙流体因子AVAZ反演

裂缝型储层表现出较强的各向异性特征.缝隙中充填不同流体时,裂缝储层的地震响应特征也不相同.本文从各向异性岩石物理模型出发,引入可有效识别缝隙流体的指示因子,并研究缝隙充填流体类型、饱和度以及缝隙纵横比与流体因子的相互关系,进而分析不同流体充填时介质的地震响应特征,并基于AVAZ反演方法估测缝隙流体指示因子.首先对缝隙流体因子的敏感性进行了分析,讨论当缝隙充填不同流体时,缝隙流体因子值的变化特征,同时研究了不同流体类型充填时裂缝储层反射系数随方位角和入射角的变化特征.某工区测井数据和复杂裂缝模型应用表明,基于各向异性岩石物理的缝隙流体因子AVAZ反演方法合理、可靠,且具有良好的抗噪性,即当对合成地震记录添加信噪比不小于1/2的随机噪声时,利用AVAZ反演方法估测所得流体因子值与真实值仍然吻合较好.     

裂缝型储层流体识别方法

裂缝型储层的描述包括预测裂缝分布特征和识别裂隙充填物.依据等效介质理论计算的纵波速度随裂缝密度的增大而减小.正演地震记录显示,裂缝介质含气时反射振幅最大,且变化程度比含油或含水时大.叠前方位AVO反演所得的各向异性梯度Bani与裂缝密度成正比,可用于描述有效裂缝发育强度.对于不同的裂缝密度,各向异性梯度Bani与各向同性梯度Biso的比值Ifluid(1)近似为常数,且对流体敏感.经裂缝纵横比和背景介质拉梅常数修正后,流体因子Ifluid既不随纵横比变化,又不受背景介质的影响,是裂缝型储层敏感的流体识别因子.在塔里木盆地塔北哈拉哈塘地区热瓦普区块碳酸盐岩储层裂缝发育区域,运用该参数在井点处的流体识别效果与钻井结果一致.     

地层模量分解及在流体识别中的应用

储层流体识别是确定油气水分布,合理布设井位,提高钻井成功率的关键之一.本文基于流体饱和孔隙介质岩石物理模型,对地震反演的地层体积模量进行分解,获得孔隙流体体积模量,并依据油、气、水（尤其是气-油、气-水）模量的显著差异进行识别.文中简要分析了Gassmann模型和Kuster-Toksöz模型的特征,详细讨论了孔隙形态和饱和度对弹性模量的影响,提出了联合Kuster-Toksöz方程和Gassmann方程的体积模量分解方法.该方法通过Kuster-Toksöz方程从测井数据中反演地层骨架固体和干骨架的弹性模量,再利用Gassmann方程对地层体积模量进行分解,既考虑了孔隙形态,又充分利用了Gassmann方程的易用性.理论模型结果表明方法是可行的.方法应用于西部地区某气田,流体识别与地层含气性预测结果与钻井基本一致,进一步证实了方法的有效性.     

基于线性贝叶斯和改进的典型相关分析法的地震岩石物理反演

岩石物理反演作为一种直观的定量解释手段, 是储层表征的一个重要研究课题, 其中岩石物理模型是联系储层物性参数与弹性参数的桥梁.传统岩石物理反演往往需要在井位处校准岩石物理模型, 而在地下介质复杂时, 常规的岩石物理模型难以准确描述二者之间的关系, 极大地影响了岩石物理反演的准确性.为降低岩石物理模型校准带来的误差, 本文引入改进的典型相关分析(BP-CCA)法来构建储层物性参数与弹性参数之间的统计岩石物理关系, 从而获得地下储层物性参数的空间展布信息.此外, 该方法采用线性贝叶斯理论从叠前地震数据反演得到纵、横波速度及密度等弹性参数, 具有较高的反演精度和计算效率.本文对提出的方法进行了合成数据实验和实际数据应用测试.结果表明, 该方法可实现对储层参数的准确刻画, 验证了其可靠性.

     

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.     

基于叠前反演的流体敏感属性实验研究及应用

提取叠前地震振幅信息的叠前反演技术已成为储层预测的重要手段,其能获得各种岩石弹性参数,丰富储层预测方法.因目标储层的差异性,优选并建立有利的流体敏感参数对储层流体检测尤为重要.本文基于岩石物理实验,测量并分析了岩石弹性参数随流体饱和度的变化特征,进一步根据岩石物理理论建立组合流体敏感参数,达到对油气检测的最佳敏感效果.定义了流体敏感量,定量分析岩石弹性参数的流体敏感性.最后本文在X区块进行了叠前地震反演的应用,结果表明通过岩石物理实验分析并建立获得的流体敏感参数能明显的提高储层的识别能力.     

孔隙、裂隙介质弹性波理论的实验研究

近年来发展起来的“孔隙、裂隙介质弹性波理论”提高了人们对实际岩石声学性质的模拟和预测的能力.作为对这一理论的实验验证和重要应用,我们将它用来模拟和解释岩石超声实验中测得的干燥和饱和岩石弹性波速度随压力的变化曲线.理论模拟的重要参数,如岩石的裂隙密度等是从实验数据反演得到的.结果表明：无论是孔隙度较高的砂岩,还是孔隙度很小的致密岩石,如花岗岩,该理论都能很好地描述岩石在干燥和饱和状态下纵、横波速度随压力的变化.造成波速变化的原因是岩石中裂隙在压力作用下的闭合和裂隙密度的减少.本文的结果还指出了将岩石裂隙密度作为描述岩石的重要物性参数,并给出了从实验室超声测量中确定这一参数的方法.     

Generalized anisotropy parameters and approximations of attenuations and velocities in viscoelastic media of arbitrary anisotropy type – theoretical and experimental aspects*

Seismic anisotropy in geological media is now widely accepted. Parametrizations and explicit approximations for the velocities in such media, considered as purely elastic and moderately anisotropic, are now standards and have even been extended to arbitrary types of anisotropy. In the case of attenuating media, some authors have also recently published different parametrizations and velocity and attenuation approximations in viscoelastic anisotropic media of particular symmetry type (e.g., transversely isotropic or orthorhombic). This paper extends such work to media of arbitrary anisotropy type, that is to say to triclinic media. In the case of homogeneous waves and using the so‐called ‘correspondence principle’, it is shown that the viscoelastic equations (for the phase velocities, phase slownesses, moduli, wavenumbers, etc.) are formally identical to the corresponding purely elastic equations available in the literature provided that all the corresponding quantities are complex (except the unit vector in the propagation direction that remains real). In contrast to previous work, the new parametrization uses complex anisotropy parameters and constitutes a simple extension to viscoelastic media of previous work dealing with non‐attenuating elastic media of arbitrary anisotropy type. We make the link between these new complex anisotropy parameters and measurable parameters, as well as with previously published anisotropy parameters, demonstrating the usefulness of the new parametrization. We compute the explicit complete directional dependence of the exact and of the approximate (first and higher‐order perturbation) complex phase velocities of the three body waves (qP, qS1 and qS2). The exact equations are successfully compared with the ultrasonic phase velocities and phase attenuations of the three body waves measured in a strongly attenuating water‐saturated sample of Vosges sandstone exhibiting moderate velocity anisotropy but very strong attenuation anisotropy. The approximate formulas are checked on experimental data. Compared to the exact solutions, the errors observed on the first‐order approximate velocities are small (<1%) for qP‐waves and moderate (<10%) for qS‐waves. The corresponding errors on the quality factor Q are moderate (<6%) for qP‐waves but critically large (up to 160%) for the qS‐waves. The use of higher‐order approximations substantially improves the accuracy, for instance typical maximum relative errors do not exceed 0.06% on all the velocities and 0.6% on all the quality factors Q, for third‐order approximations. All the results obtained on other rock samples confirm the results obtained on this rock. The simplicity of the derivations and the generality of the results are striking and particularly convenient for practical applications.     

Rock-physics forward modelling to predict seismic behaviour: A case study for exploration target in Mahanadi basin,East Coast of India

One of the major aspects of rock-physics forward modelling is to predict seismic behaviour at an undrilled location using drilled well data. It is important to model the rock and fluid properties away from drilled wells to characterize the reservoir and investigate the root causes of different seismic responses. Using the forward modelling technique, it is possible to explain the amplitude responses of present seismic data in terms of probable rock and reservoir properties. In this context, rock-physics modelling adds significant values in the prospect maturation process by reducing the risk of reservoir presence in exploration and appraisal phases. The synthetic amplitude variation with offset gathers from the forward model is compared with real seismic gathers to ensure the fidelity of the existing geological model. ‘Prospect A’ in the study area has been identified from seismic interpretation, which was deposited as slope fan sediments in Mahanadi basin, East Coast of India. The mapped prospect has shown class-I amplitude variation with offset response in seismic without any direct hydrocarbon indicator support. The existing geological model suggests the presence of an excellent gas reservoir with proven charge access from the fetch area, moderate porosity and type of lithology within this fan prospect. But, whether the seismic response from this geological model will exhibit a class-I amplitude variation with offset behaviour or ‘dim spot’ will be visible; the objective of the present study is to investigate these queries. A rock-physics depth trend analysis has been done to envisage the possibilities of class-I reservoir in ‘Prospect A’. Forward modelling, using a combination of mechanical and chemical compaction, shows the synthetic gas gathers at ‘Prospect A’, which are class I in nature. The study has also depicted 2D forward modelling using lithology and fluid properties of discovery well within similar stratigraphy to predict whether ‘dim spot’ will be seen in seismic. The estimated change in synthetic amplitude response has been observed as ∼5% at contact, which suggests that the changes will not be visible in seismic. The study connects the existing geological model with a top-down seismic interpretation using rock-physics forward modelling technique to mature a deep-water exploratory prospect.     

龙马溪组页岩微观结构、地震岩石物理特征与建模

龙马溪组页岩是目前国内页岩气勘探的主要层位之一. 由于岩石物理实验结果具有区域性, 龙马溪组页岩的岩石特征与其地震弹性性质的响应规律需要开展相关的实验和理论研究工作予以明确. 本研究基于系统的微观结构观察(扫描电镜和CT成像技术)和岩石物理实验来分析龙马溪组页岩样品地震弹性性质的变化规律, 并依据微观结构特征建立相应的地震岩石物理表征模型. 研究结果表明, 石英含量对龙马溪组页岩的孔隙度以及有机碳(TOC)含量具有一定的控制作用, TOC和黄铁矿主要赋存于孔隙中; 岩石骨架组成亦受控于石英或粘土含量, 在石英含量大于40%(对应粘土含量小于30%)时, 以石英、粘土共同作为岩石骨架, 而粘土含量大于30%时, 则以粘土作为岩石的骨架. 因此, 岩石骨架组成矿物、TOC含量、孔隙度共同制约龙马溪组页岩的地震弹性性质, 富有机质储层岩石通常表现出低泊松比、低阻抗和低杨氏模量的特征, 但由于支撑矿物的转换, 某些富有机质页岩亦可表现为高阻抗特征. 粘土矿物的定向排列仍然是造成页岩样品表现出各向异性的主要原因, 各向异性参数与粘土含量具有指数关系. 基于龙马溪组页岩的岩性特征及微观结构特征, 可以利用自洽模型(SCA)、微分等效模量模型(DEM)和Backus平均模型的有效组合较为准确地建立龙马溪组页岩的地震岩石物理模型, 实验结果和测井数据验证了模型的准确性.研究结果可为龙马溪组页岩气储层的测井解释和地震"甜点"预测提供依据.     

基于叠前地震数据和岩石物理的游离气定量估算方法——以印度Krishna-Godavari盆地NGHP01-10A井为例

天然气水合物稳定带下方游离气分布模式、气体含量及其对水合物富集成藏的指示是水合物研究中的难点,而利用振幅随偏移距变化(Amplitude Versus Offset, AVO)与岩石物理模型能够对游离气含量进行地震定量解释.我们对印度Krishna-Godavari (K-G)盆地的地震资料进行了叠前保幅处理,在测井数据和层位标定的基础上,基于等效介质岩石物理模型和AVO正演模拟定量估算了NGHP01-10A井的游离气饱和度,发现水合物下方的游离气饱和度与其分布模式有关.游离气呈均匀分布时饱和度为孔隙空间的0.3%~0.4%,而块状分布时为3%~4%,该结果与NGHP01-10D实测计算的泊松比交汇分析结果吻合很好.最后再根据干燥岩石骨架的泊松比反演结果进一步判断游离气分布为均匀分布,其饱和度为0.3%~0.4%.     

EI二阶导数的储层参数和流体模量反演方法

储层孔隙度、泥质含量及流体类型估测是地球物理勘探的重点及难点问题.基于岩石物理理论及等效模型,可以构建油气储层反射特征与储层孔隙度、泥质含量及流体的映射关系.本文从流体替换模型出发,结合矿物平均模型,首先推导了以孔隙度、泥质含量、流体模量和密度表征的非线性反射系数及弹性阻抗公式;然后根据推导的反射系数和弹性阻抗公式,建立了一套两步法反演策略：利用部分角度叠加数据进行线性反演预测弹性阻抗体;利用预测的弹性阻抗体开展泥质含量、孔隙度、流体模量和密度等变量的非线性反演,引入弹性阻抗对于反演变量的一阶和二阶导数以提高反演的精度.最后,利用层状模型验证了新推导的反射系数方程的精度,并分别利用测井数据模型生成的含噪声合成地震记录及实际工区地震数据验证了所提出的反演方法的可靠性.

     

Drained-to-undrained transition of bulk modulus in fluid-saturated porous rock induced by dead volume variation

We examine the effect of poroelastic boundary conditions when determining elastic properties of fluid-saturated porous rocks from forced-oscillation laboratory experiments. One undesired yet often unavoidable complication in the estimation of the undrained bulk modulus is due to the presence of the so-called dead volume. It implies that some fluid mass can escape the rock sample under applying a confining pressure perturbation. Thus, the dead volume compromises the undrained state required to unambiguously determine the undrained bulk modulus. In this paper, we model data of recently performed low-frequency (0.1 Hz) measurements. Therein, the dead volume has been systematically varied from 10% to 1000% of the pore volume. For the smallest dead volume, the inferred bulk modulus is close to the Biot–Gassmann undrained bulk modulus. With increasing dead volume, the experimentally inferred bulk modulus approaches the drained bulk modulus. We show that the transition from undrained to drained state as a function of dead volume can be modelled with a 1D poroelastic model for the rock sample-dead volume system with a boundary condition that honours the continuity of the fluid volume flux. We discuss the limitations of the 1D model when applied to data recorded at higher frequencies (up to 100 Hz).